Hey Vsauce, Michael here. You probably think that Iraqi government is stable and legitimate, well think again, there are multiple claims and today we are going to ignite them and see how many new countries will pop up on the map.
How to get your maths answer: 1. Ask any asian friend (preferably Chinese or Indian) 2. If that doesn't work ask your teacher... 3. You're in a test? Try and remember this video you watched 9 months ago 4. Wait... nvm I can just Google it...
No, it’s just that no one had come up with one back then. And honestly, the trick that Michael shows in this video isn’t a quick rule at all. Very time consuming. At that point it is faster to just divide the number by 7.
@@davidcole2913 I have a book from 1960 that shows a divisibility by 7 rule, though it's sort of complex. You have to match up six digits in the number to the series 132 645, working from the rightmost digit first. If your number is larger than six digits you start the 132 645 series again. Each digit in the series is multiplied by the corresponding number in the answer. For 362,880, working from the right, you'd get (1x0) + (3x8) + (2x8) + (6x2) + (4x6) + (5x3) = 91. Then you divide THAT by 7 and get a zero remainder. I think it's easier to just divide the number by 7 straight through, especially if you are doing the problem mentally.
@@jeffw1267 @jeffw1267 Double the last digit and subtract it from the remaining digits. Ex. 434 => 43 - 2(4) = 35, which is 7x5, so 434 is divisible by 7. Using Michael's method, 1/10(abc - c) - 2c 0.1abc - 0.1c - 2c 0.1abc - 2.1c 10(0.1abc - 2.1c) = abc - 21c 21c is just 7(3c), so it checks out.
I've been using these divisibility rules my entire life in school and never knew how they worked. Who'd have thought that their functioning would be so easy to understand. Thanks Michael, very cool 👏👏
Divisibility by each number: 2: Number is even i.e. last digit is 2,4,6,8,0 3: Sum of digits is a multiple of 3 4: Last 2 digits divisible by 4 5: Last digit is a 5 or a 0 6: Number is even and Sum of digits is a multiple of 3 7: Take 5× last digit and add to remaining digits OR take 2× last digit and subtract from remaining digits. Final total divisible by 7 8: Last 3 digits are divisible by 8 9: Sum of digits is a multiple of 9 10: Last digit is a 0 11: Alternate between Adding/Subtracting digits from left to right starting with Subtracting. Final value is 0 or divisible by 11 12: Last 2 digits divisible by 4 AND Sum of digits is a multiple of 3
@@natant927 It's because 6 has a factor of 2 ie. 6 = 2 * 3. This means that if a number is divisible by 6 then it must be even so it doesn't make sense to repeat the divisibility by 2 rule
@@aryyancarman705 it did kinda called dong something you can Do Online Now Guys Before it was reffering to uhhh the thing and its called ding now. I think anyways lol
There's a trick for 7 that's even easier: Separate the ones digit from the rest, double the ones digit, then subtract the 2 numbers. Here are some examples 903 separates into 90 and 3, double 3 to get 6, 90 - 6 = 84 which is divisible by 7. (903 = 7 x 129) 3171 separates into 317 and 1, double 1 to get 2, 317 - 2 = 315, which splits into 31 and 5, double 5 for 10, 31-10=21 which is divisible by 7. (3171 = 7 x 453) Note: If this process gives you 0, the original number is also divisible by 7
Oohhh, this is interesting. I suppose this is because adding -2 is the same as adding 5 modulo 7. As far as 7 is concerned, this is essentially the same as adding 5 times the last digit. Brilliant!
eventhorizon51 The reasoning is very similar. I am going to use three digits for the sake of simplicity for this proof, but it trivially generalizes to any number of digits larger than 2 via induction. Any 3-digit number is given by x = 100d(2) + 10d(1) + d(0), where d(i) is between 0 and 9 inclusive, except for d(2) excluding 0. The proposed method is 10d(2) + d(1) - 2d(0), but it works because 10d(2) + d(1) = (100d(2) + 10d(1))/10 = (100d(2) + 10d(1) + d(0) - d(0))/10 = (x - d(0))/10, and (x - d(0))/10 - 2d(0) = x/10 - 2.1d(0) = (x - 21d(0))/10, and 21 is divisible by 7.
This is also a much more useful shortcut if for some reason you don't have a calculator on hand. The one shown in the video is cool and all, but it's not very user friendly for larger numbers, not to mention having a bit of a complex process to it. This is a lot simpler and easier to follow.
@@Aw3som3-117 I suppose only having to multiply by two will generate easier computations, so it might be slightly easier and faster than Michael's method.
@@kickowegranie3200 That is true, because 8 and 9 are not primes, and can thus be written has factors of the previous numbers, thus 7! is divisible by those as well.
We can create multiple methods to solve the 7 one. Like multiplying unit digit by 1.5 and adding it to the rest should also work bcoz 1.5 - 0.1 is 1.4 But using whole numbers like 2 or 5 makes more sense I agree
You can also, for example if the number is abcdefgh, look at h+3*g+2*f-e-3*d-2*c+b+3*a. Basically, going from the least significant to most significant digit you just repeat 1, 3, 2, -1, -3, -2. Much easier to do than the method shown in the video. As a bonus, all the other divisibility rules also preserve the remainder when divided by that number(for example, the sum of digits of 582 is 15 so it has a remainder of 6 when divided by 9). The rule for 7 shown in the video doesn't preserve the remainder, but this one does(but keep in mind that the remainder of -1 is 6, not 1).
Not related message from a random Hongkonger for anyone watching: Remember the Virus is creating in China, it is all okay to call it China Virus. Never trust WHO cuz it is controlled by CCP.
Yup, let's study to keep graduation possible (ahem homeschool) - internet available - free will available - no teacher peeking for rule breaking - school rules : no rules, games
@@CRAIGC55 Well, then people must feed animals the right way, make special meal schedules, and redo the FRIKKING BIOLOGI, viruses are here because they are predictors too, imagine life 200 000 years ago but in the kingdom of bacteria, viruses, cells, whatever nothing has changed
@@mrghostlyr1162 Viruses thrive off of bad cells. If you have been eating dirty for years, you will be a breeding ground for illness. If you remove the bad cells, virus has nowhere to live. Minimal place to live at best.
This is the first time even in my life im watching a pure math video not because of school but because I wanted to... WOW, Michael really is powerful lmao
Michael thank you for all of your Vsauce, Mindfield and Ding videos! The content is some of the most fascinating stuff I've watched on the whole internet. Your method of presentation and your subtle humor makes for a really enjoyable experience.
My favorite part of my Number Theory elective in college was proving the divisibility rules for 3 6 and 9. They seem so not math-y when you learn them as a kid, but the proof is very easy to understand
Ok I'm kinda embarassed to ask this but... so I'm pretty good at english becouse I'm learning it since I was 6 but I still don't understand what "Or do I" meme means
@@antonioocchipinti801 No need to be embarrassed about that! It's something Michael say A LOT in his videos. That's all! 😃 Watch a few more from VSauce and you'll see what we're talking about!
antonio occhipinti the ‘or do i?’ meme uses sarcasm. Sarcasm is a type of humour that becomes funny by doing something unexpected. Like saying (insert random dictator here) did nothing wrong. The joke teller doesn’t think that that person did nothing wrong, but its so unexpected and rude that it becomes funny.
8:31 explains the 3 rule. 11:11 explains the 4 rule. 13:27 explains the 8 rule. 15:40 explains the 7 rule. 1, 2 and 5 are obviously why they work. 5 is always 5 or 0. 2 is all the even number. And 1 is all the entire numbers that exists. 6 is 2 times 3, so it's obviously why we need to use the 3 rule and see if is even. (The digital root of a number is sum all its digits and if this new number has more than one digit sum it again until you have only one digit which will be the digital number) And the digital root of any number multiple of 9 must be 9. Because 9 is the only number that don't change the result of a digital root. and mustn't be any number that change the original 9 in the digital root. For example 729=7+2+9=18=1+8=9 But 3729=3+7+2+9=21=2+1=3 And as you can see here: 73649163=3 73649163 *9* =3. 9 don't change the digital root. Also I wanna say it's because 9 add 1 ten and put out 1 unit so 9 don't change anything the value. (Idk if the digital root rule is the correct way of show why it works but I always have that theory and it works so you can explain it in that way)
At first I thought he was talking about all of us watching this video together. More and more, I am convinced that Michael is talking about the math itself. The math is our new math friends.
I go back and watch this video over and over again simply because the explanations for how it all works is absolutely beautiful, and of course Michael talking about anything always makes it better too
Michael! I though of a way faster method to check divisibility by 7: 1. Take the leading two digits of the number. 2. Divide by 7 and find the remainder. 3. The remainder becomes the new leading term 4. Repeat until you recognize the number as divisible by 7 or not. E.g. 362,880: Not sure if divisible by 7 36->1 12,880: Not sure 12->5 5,880: Not sure 58->2 280: Pretty sure 28->0 0: Divisible by 7
Divisibility in base 6: *1* If the number ends in the ones place, then the number is divisible by 1. (same as 1 in base 10) 1:08 *2* If the number ends in 0, 2, or 4, then the number is divisible by 2. (same as 2 in base 10) 1:14 *3* If the number ends in 0 or 3, then the number is divisible by 3. (same as 5 in base 10, but replaced by 3) 1:17 *4* If the sum of the ones place digit and the double of the tens place digit is divisible by 4, then the number is divisible by 4. (same as 4 in base 10) 3:17 *5* If the sum of the digits is divisible by 5, then the number is divisible by 5. (same as 9 in base 10, but replaced by 5) 2:29
The way I was always taught to find a multiple of 7 is to double the last digit and subtract it from the rest of the number. 14 = 8 - 1 = 7 49 = 18 - 4 = 14 = 7 798 = 79 - 16 = 63 = 7
don't abuse the equal sign like that You can do this 7 | 63 "7 divides 63" or for the other way around, "63 dibisible by 7" i remember using in school three vertical dots like 63 :7 but with this unicode character VERTICAL ELLIPSIS (U+22EE) lookup the code. or like this 63 % 7 = 0 (modulo operation result )
@@Dm3qXY - It would have been far too long to type what I wanted to say, and I'm just here for fun... I think it makes enough sense once the numbers get smaller.
Because 200 is evenly divisible by 8, there is an alternate way to check for divisibility by 8. Given last digits: ...abc, find 2b+c as you did with 4, but if a is odd, add 4, if a is even, ignore it. If (2b+c +[4, if and only if a is odd]) is divisible by 8 then the original term is divisible by 8 as well.
o o o o o o o o o o o o o o o o o o o o o_ o o o o o o o o o o o o o o o o o o o o o_ o o o o o o o Seven rows and seven columns. Count the o's and then you've got 'em.
Not exactly a divisibility rule, but: To check if a number is prime, you only have to check all primes up to its square root. For example: is 103 prime? It’s square root is between 10 and 11, so check 2, 3, 5, and 7. We know it’s odd and doesn’t end in 5 or 0, and that 1+0+3 =4. The only one left is 7, which we test with the trick in the video: 10 + 5(3) = 25, so 103 is not divisible by 7 and is therefore prime.
@@akkok5059 First why do we only check divisibility with prime numbers? Because non prime numbers can be written as the product of prime numbers. Why is that? Because if your number is divisible by a non prime number, you can divide the factor once more until only prime numbers remain. For example, let's take 20. 20=2×10. But 10 is non prime which means you can divide it. 10=2×5. In the end, 20=2×2×5. You only need to check prime numbers to know if your number is prime. The only prime numbers below 10 are 2, 3, 5 and 7.
@@akkok5059 Because the rest of numbers between 1 and 10 are product of primes. Take the number 103 and check divisibility by 2, then 3. Now we have 4, but if the number is divisible by 4 then it's also divisible by 2 and we checked that already. Next comes 5, then 6 but if the number is divisible by 6 then it's also divisible by 2 and 3 - we checked that already.
Actually, there are divisibility tests for 7 that are simpler provided you have a fixed number of digits to work with. For example, if I want to work with 3 digits, then any number will expressible as 100a + 10b + c. 98a + 7b will always be divisible by 7, because 98 is divisible by 7, since 98 = 70 + 28, and 28 is divisible by 7. Therefore, one only need check if 2a + 3b + c is divisible by 7 to check if your 3-digit number is divisible by 7. The problem is that this does not generalize as easily to any other number of digits. For example, if you want to check for 4 digits, as in 1000a + 100b + 10c + d, you instead have to check if 6a + 2b + 3c + d is divisible by 7. In other words, the quantity you have to check depends on the number of digits. This does not require recursion, but it trades for having infinitely many rules, one for each number of digits.
@@angelmendez-rivera351 i was gonna say calm down its just a joke but that's actually a really cool point. It's not immediately obvious why 7 causes so many issues
@@melovepeas The reason is that 7 is prime, and thus coprime with 10 (it shares no common factors with 10 other than 1). But, you say, it works with multiples of 3 ! And that's because 10 is 1 away from a multiple of three, which is actually a very special thing. Basically, there's no general rule... unless there is one. That is, it only works in special cases and in general you just have to go the recursive route. It's amazing how many things we take for granted about numbers when a lot of properties we think as intrinsic to the numbers themselves are actually dependent on the base being used.
Michael: "...But how do these tricks work?" Music: "..." Me: "...Wait, what- nothing??? Wow, I have never felt the absence of the Vsauce music so keenly..."
I remember watching this when it came out. I didn't understand it back then but now after some algebra, and now calculus, This actually makes a lot of sense.
Michael: now let’s see if it’s divisible by four. My brain: oh yes, we can half it twice. Michael: take the first number in the two digit number and double then add it to the second digit. Me:...
For those of you who forgot the rules as soon as you stopped watching: 2: If the number is even, it can be divided by 2 3:Take all the digits in a given number and sum them up. If the resulting number is divisible by 3, the original number is divisible by 3 4: If the last 2 digits of the number form a number that is divisible by 4, the whole number is. OR. Take the 10s digit and double it, and then add to that the ones digit. If that number is divisible by 4, the original number is as well. 5: If the number ends in 0 or 5, it's divisible by 5 6: If the number is divisible by 3 and is even, it is divisible by 6 7: Take the 1s digit, and multiply it by 5. Then, add to it the remaining numbers as if it were its own number (the whole thing, not each individual digit). If the resulting number is divisible by 7, the original number is as well. 8: Take the hundreds digit, and multiply it by 4. To that, add the tens digit times 2. To that, add the ones digit. If the resulting number is divisible by 8, the original number is divisible by 8. 9: If the sum of all of the digits in a number is divisible by 9, the original number is divisible by 9 REMEMBER: All of these processes can be done multiple times if you are unsure if the resulting number is divisible by the number (1, 2, 3... ,9)
i learned a lot of these as a kid and one favorite pastime of mine is to mentally add the digits on license plate numbers to determine whether or not they're divisible by 9 (license plates in my country always have a 4 digit number in them)
This is exactly what I needed. The finals from last semester were delayed and they'll be soon, and this is a perfect way to remind myself about divisibility rules.
@@rjkzk If "That Guy" can help me out please, I'm trying to learn more about the english language. Technically that's not more than one second, so should it be "0.1354 second"?
Relevant trivia: The number 2520 is the smallest number that's divisible by 1-10. Edit: It also has many other interesting properties such as being: - half of 7! (7 factorial) - a highly composite number (if you don't know what that is you may want to watch this video: ruclips.net/video/2JM2oImb9Qg/видео.html) - a colossally abundant number (I've tried to find and video or website that explains it in an understandable way but I can't find one) - a Harshad number (a number that is divisible by the sum of its digits. Ex. 24: 2+4=6, and 24 is divisible by 6) - the aliquot sum of 1080 (a rare relationship between two numbers where the sum of one of their factors is equal to the second number and the sum of the factors of the second number is equal to the first number. If I didn't explain it well I recommend watching until 1:30 of this video: ruclips.net/video/WtbkBl7ct4I/видео.html)
@Wouter vanR I prefer Tau over Pi but I kind of feel bad for Pi this year; nearly everyone forgot about Pi day because of the coronavirus Edit: grammar
The divisibility rules for all powers of 2 stem from the divisibility by 2 rule. The general power of 2 divisibility rule is this: For any 2^n power divisibility, take the last n digits and sum up this series: 2^(n-1) * 1st digit + 2^(n-2) * 2nd digit ... + nth digit and check if the sum is divisible by 2^n. If you don’t know yet, repeat until you figure out if it’s divisible by 2^n.
Divisibility rules of 4, 8, 10, 11, 15, 20, 30 or 50: 4: If the number is divisible by 2 twice. 8: If the number is divisible by 2 thrice. 10: If the number ends in 0, it is. 11: If the sum of the odd positions of the number minus the sum of the even positions of the number is 0 or multiple of 11 (abcd-> (a+c)-(b+d)= 0 or multiple of 11) 15: If the number is divisible by 3 and 5. 20: If the number is divisible by 2 and 10. 30: If the number is divisible by 3 and 10. 50: If the number is divisible by 5 and 10.
Bonus divisibility rule: To determine if something can be divided by 11, take off the last 2 digits and add them to the remaining number. Repeat until you have something that you know is divisible by 11. Ex: 35,365 353 + 65 = 418 4 + 18 = 22 = 2 × 11 Bigger ex: 6,954,035 69,540 + 35 = 69,575 695 + 75 = 770 7 + 70 = 77 = 7 × 11 Explanation: Number abc, last 2 digits are bc. abc = a × 100 + bc The operation does: (abc - bc + (100 × bc)) / 100 Essentially, you're adding 99 × bc to the number, since 99 × is always divisible by 11. However subtracting 1× and adding 100× does the same thing, so you can use that instead.
Simpler method: Add the 1st, 3rd, 5th ........ digits together and the 2nd, 4th, 6th digits together and subtract the two. If you get a multiple of 11 or 0, it is divisible by 11. Ex- 35,365 Sum of odd digits = 3 + 3 + 5 = 11 Sum of even digits = 5 + 6 = 11 Difference = 0 Therefore divisible by 11
I have a more interesting trick. Just substract the last digit from the rest of the number. If the result is divisible by 11, then so is the original number. Ex. 35365 3536-5=3531 353-1=352 35-2=33 3-3=0 0 is divisible by any number except itself, so it's obviously divisible by eleven, and so is 35365
Legit did the same thing. I routinely eat snacks or meals while I watch videos, but opted out of doing that with this one so I could pay attention to it.
Also, popcorn with a capital "P", which implies it's either someone's name, or a place's name. You can't carry a place around -or can you?- , so I guess they watched with a friend?
I got halfway through the video and Michael is showing us why these tricks work , I began to realize that this is how I do work in my head instead of writing it all down. this is the way I simplify the work so that I can do it in my head instead of having to work it all out on paper
As someone with dyscalculia, this is INCREDIBLY helpful. I wish Micheal had been my math teacher! I need to understand HOW math works, otherwise it's too abstract for me. When I was a kid we were expected to just memorize everything by rote with zero explanation, so even as an adult I still struggle with basic multiplication and division. Logic and algebra make more sense to me, so this video is a life saver!
Math should _only_ be about understanding how things work. There should be hardly any memorization at all. It sounds like your difficulty with math had more to do with poor teaching methods.
I feel like my foundation for maths were scrambled by just that. We were always taught to memorize recipes rather than understand how they actually work. I wish I hadn't been taught this way.
What if I told you this video *severely* overcomplicates things? I suggest reading about the cyclic groups and modular arithmetic. Makes all these results much more basic and really easy to extend to other numbers.
Развлечения
Schools: *close*
Michael: ...or do they???
*Vsauce music starts playing*
Sh1pp0K1tsune It started playing before I even read your comment. X)
DING!!!!!!!!!
My literal exams: Cancelled
Michael: Or are they?
@@TuhinBagh dong
Michael: "It's so important to unify, but today we're going to divide."
*Starts multiple civil wars.*
Yeet
Hey Vsauce, Michael here. As we all know, slave trade is unhumanitarian and unethical, and we should band together to abolish it.
*Or should we?*
fun fact: division in Swedish is called "bråk" which also means brawl or fight
Hey Vsauce, Michael here. You probably think that Iraqi government is stable and legitimate, well think again, there are multiple claims and today we are going to ignite them and see how many new countries will pop up on the map.
You mean divisible civil wars
Michael: Is 80 divisible by 4?
Me: I don't know. Let me ask my French friends...
hon hon, it is la weed nombre.
Michel just missed a great opportunity to speak about ... you know, the big white Elephant in the room... THAT.
How to get your maths answer:
1. Ask any asian friend (preferably Chinese or Indian)
2. If that doesn't work ask your teacher...
3. You're in a test? Try and remember this video you watched 9 months ago
4. Wait... nvm I can just Google it...
@@user-xw4mu6nz4t and if that doesn't work be inspired by the meet the engineer SFM and solve it with a gun, and if that don't work try more gun.
Quatre-vingt ;)
BRO when I was in elementary school we did all of these except we got told “there’s no rule for divisible by 7” they LIED!!
No, it’s just that no one had come up with one back then. And honestly, the trick that Michael shows in this video isn’t a quick rule at all. Very time consuming. At that point it is faster to just divide the number by 7.
15:38 here we are
We were told that it was too critical for us so they excepted...
@@davidcole2913 I have a book from 1960 that shows a divisibility by 7 rule, though it's sort of complex. You have to match up six digits in the number to the series 132 645, working from the rightmost digit first. If your number is larger than six digits you start the 132 645 series again. Each digit in the series is multiplied by the corresponding number in the answer. For 362,880, working from the right, you'd get (1x0) + (3x8) + (2x8) + (6x2) + (4x6) + (5x3) = 91. Then you divide THAT by 7 and get a zero remainder. I think it's easier to just divide the number by 7 straight through, especially if you are doing the problem mentally.
@@jeffw1267 @jeffw1267 Double the last digit and subtract it from the remaining digits. Ex. 434 => 43 - 2(4) = 35, which is 7x5, so 434 is divisible by 7.
Using Michael's method,
1/10(abc - c) - 2c
0.1abc - 0.1c - 2c
0.1abc - 2.1c
10(0.1abc - 2.1c)
= abc - 21c
21c is just 7(3c), so it checks out.
"divisibility rules"
glad to see micheal sticking up for the underrated mathematical operation
lonely_ space_ egg I’m more of a fan of roots
Tristen Roddenberry idk man it’s all about quadratics imo
Pepper Mint Nah logarithms are where it’s at
Excuuuse you princess. Division is probably the most rad basic mathematical operation
@uwau cube root of 24 the 2.88th Reich :D
Schools: *close*
Michael: Fine, I’ll do it myself
this is a lesson on "discrete math" from college by the way.
Fine, I'll do it BETTER myself*
ngl I learned new interesting stuff and I'm in high school
He will not divide us
990 likes
Vsauce is that one mad scientist that makes everything fun, but at the same time everyone suspects him of being on crack.
Same for Micheal Reeves tbh
Maybe to people who have never seen a real crackhead before 😅💯
@@noctusion2392 nah it doesn't feels the same he's crazy in his own way
wait he isn't on crack?
@@matttacoor is he
"Why Did They Change Math!? MATH IS MATH!" - Mr. Incredible.
This turned into a math channel so progressively that I didn't even notice.
JJJ he’s literally numberphile rn
It was supposed to be a channel with fun links in the description
@@cheesycheese60 maybe 5 years ago
@@Ptaku93 u know time goes fast
@@Ptaku93 Well... no. The name literally means "Do Online Now Guys".
Michael is starting to look like Charles Darwin with that beard
Charles Manson*
Well, he is the next step in evolution for humankind.
Michael is Charles Darwin reincarnate
Or Friedrich Engels
Yes he is almost ready for the prophecy
Two types of people:
Those who write '8' in a single stroke
Those who draw two circles
I draw 8 with a single stroke, obviously.
the 2 types are
1. those who write it in one stroke
2. michael david stevens
It just comes out as nicer looking when you clearly make two circles. Unless they’re too far apart... or an accidental venn diagram...
What if I drew the two other halves of it
I prefer to make a 3 and a backwards 3, please, I have standards
I've been using these divisibility rules my entire life in school and never knew how they worked.
Who'd have thought that their functioning would be so easy to understand.
Thanks Michael, very cool 👏👏
He's acting like he didn't leave us hanging for 7 months
- Leg1t Lmao
He did have the holes one on Vsauce
Oh god I've just realized as well
The hero we need right now, but not the one we deserve...
Junior Studios Nobody truly deserves Michael..
why is it in past-tense?
Mister past tense there is probably feeling lonely. Be kind.
deserve*
Guðmundur Ingi Guðmundsson ok boomer
Mike: chooses 362,880 at "random"
Me who watches numberphile: I see what u did there.
???
@@shadrackbrentuo3665 the number has 160 divisors, is the factoral of 9, is a tau number, is pseudo perfect, etc.
@@shadrackbrentuo3665 basically all digits 1-9 are factors of 362880
@@honeybee9455 Ooh. Thanks!
@@shadrackbrentuo3665 np
Divisibility by each number:
2: Number is even i.e. last digit is 2,4,6,8,0
3: Sum of digits is a multiple of 3
4: Last 2 digits divisible by 4
5: Last digit is a 5 or a 0
6: Number is even and Sum of digits is a multiple of 3
7: Take 5× last digit and add to remaining digits OR take 2× last digit and subtract from remaining digits. Final total divisible by 7
8: Last 3 digits are divisible by 8
9: Sum of digits is a multiple of 9
10: Last digit is a 0
11: Alternate between Adding/Subtracting digits from left to right starting with Subtracting. Final value is 0 or divisible by 11
12: Last 2 digits divisible by 4 AND Sum of digits is a multiple of 3
😮🤯
Why cant 6 * 2 be used to verify 12😭
@@natant927 It's because 6 has a factor of 2 ie. 6 = 2 * 3. This means that if a number is divisible by 6 then it must be even so it doesn't make sense to repeat the divisibility by 2 rule
Michael looks like he's been isolated since way before this epidemic
So do I tho. Oh wait. But I have been isolated for far longer. Never mind...
He has prepared for the random chimp event well. This man will leads us to victory against the chimps
Mind Field S1 E1.
*pandemic
That would explain the 25 minute video on divisiblity rules... this man is clearly going insane
11:46
“179200 I just made this one up” people he can create numbers he’s more powerful than we thought
Wat
@@numberdballer Until he made it, 179200 did not exist.
@@LeafShade tbh i never thought about 179,200 before this video so id believe it.
Exactly
The other number was a decoy!
Michael: Writes 1792
Ramanujan: *anger intensifies*
Can you explain the joke please edit-I got it I guess he should have written 1729 because it is Hardy-Ramanujan number
?
@@hhahah7263 it's a joke about hardy-ramanujan number which is 1729
@@aryarathod9192 idk what a hardy-ramanujan even is
@@hhahah7263 It is the smallest number which can be expressed as the sum of two different cubes in two different ways
There is something really cool in the inconsistency of Michael's writing. Sometimes he writes multiplication as an x and sometimes and dot. very cool.
he probs also holds the world record for the most ways to write an 8
Michael looks like he already has been in quarantine for 5 months
he never met other humans, he was always in quarantine
BRUH LOL
He was in prison
@@QuicksolutionsOnline based
actualy 12 years
D!ng dong
Who’s there?
Vsauce
Vsauce who?
Vsauce, Michael here
Wasnt this channel called dong?
@@br6768 it was, but RUclips wasn't happy about it.
@@br6768 what dong?
It was never called dong, trust me..
@@aryyancarman705 it did kinda called dong something you can Do Online Now Guys
Before it was reffering to uhhh the thing and its called ding now. I think anyways lol
frostonium He was joking. As though the channel once being called dong was something that couldn’t be talked about.
Thank you for explaining not only "how" more importantly "why".
1:36 "First let's pick a number completely at random"
Michael lied as naturally as he breathed
Literally 9!
There's a trick for 7 that's even easier: Separate the ones digit from the rest, double the ones digit, then subtract the 2 numbers. Here are some examples
903 separates into 90 and 3, double 3 to get 6, 90 - 6 = 84 which is divisible by 7.
(903 = 7 x 129)
3171 separates into 317 and 1, double 1 to get 2, 317 - 2 = 315, which splits into 31 and 5, double 5 for 10,
31-10=21 which is divisible by 7.
(3171 = 7 x 453)
Note: If this process gives you 0, the original number is also divisible by 7
This is the one I know
Oohhh, this is interesting. I suppose this is because adding -2 is the same as adding 5 modulo 7. As far as 7 is concerned, this is essentially the same as adding 5 times the last digit. Brilliant!
eventhorizon51 The reasoning is very similar. I am going to use three digits for the sake of simplicity for this proof, but it trivially generalizes to any number of digits larger than 2 via induction.
Any 3-digit number is given by x = 100d(2) + 10d(1) + d(0), where d(i) is between 0 and 9 inclusive, except for d(2) excluding 0. The proposed method is 10d(2) + d(1) - 2d(0), but it works because 10d(2) + d(1) = (100d(2) + 10d(1))/10 = (100d(2) + 10d(1) + d(0) - d(0))/10 = (x - d(0))/10, and (x - d(0))/10 - 2d(0) = x/10 - 2.1d(0) = (x - 21d(0))/10, and 21 is divisible by 7.
This is also a much more useful shortcut if for some reason you don't have a calculator on hand. The one shown in the video is cool and all, but it's not very user friendly for larger numbers, not to mention having a bit of a complex process to it. This is a lot simpler and easier to follow.
@@Aw3som3-117 I suppose only having to multiply by two will generate easier computations, so it might be slightly easier and faster than Michael's method.
Michael: Lets pick a random number
also Michael: **picks a number divisible by all numbers 1 through 9**
he could have gone with smaller one, 7! (5040), it's also divisible into all the numbers 1-9 but it's much much smaller
@@kickowegranie3200 Or an even smaller number, 7!/2.
I think Micheal found the number himself and did not Google it. This is why he picked it I think.
@@kickowegranie3200 That is true, because 8 and 9 are not primes, and can thus be written has factors of the previous numbers, thus 7! is divisible by those as well.
@@dzarko55 which is the smallest (2520).
Michael: Draws his 8 like that
Everyone: Oooooooooooof no
what's wrong with his 8s lol
That's how they teach us to draw them in the Navy.
In Divisibility with 7,
I subtract 2 x (one's digit) instead of adding 5 x (one's digit).
It is easy to calculate and works!
Came here to say the same thing.
We can create multiple methods to solve the 7 one.
Like multiplying unit digit by 1.5 and adding it to the rest should also work bcoz 1.5 - 0.1 is 1.4
But using whole numbers like 2 or 5 makes more sense I agree
You can also, for example if the number is abcdefgh, look at h+3*g+2*f-e-3*d-2*c+b+3*a. Basically, going from the least significant to most significant digit you just repeat 1, 3, 2, -1, -3, -2. Much easier to do than the method shown in the video.
As a bonus, all the other divisibility rules also preserve the remainder when divided by that number(for example, the sum of digits of 582 is 15 so it has a remainder of 6 when divided by 9). The rule for 7 shown in the video doesn't preserve the remainder, but this one does(but keep in mind that the remainder of -1 is 6, not 1).
It took a pandemic to see him around again on this channel. Nostalgia for isolation Michael???
Blue Shirt Wow bruh it didn't appear on my sub feed
Damn we should have these pandemics more often
it’s not nostalgia it’s trauma
Not related message from a random Hongkonger for anyone watching:
Remember the Virus is creating in China, it is all okay to call it China Virus.
Never trust WHO cuz it is controlled by CCP.
Other youtubers: "Corona virus!"
Clearly superior vsauce: "divisibility tricks"
Yup, let's study to keep graduation possible (ahem homeschool)
- internet available
- free will available
- no teacher peeking for rule breaking
- school rules : no rules, games
If people ate right they wouldn't have to worry about any virus.
@@CRAIGC55 Well, then people must feed animals the right way, make special meal schedules, and redo the FRIKKING BIOLOGI, viruses are here because they are predictors too, imagine life 200 000 years ago but in the kingdom of bacteria, viruses, cells, whatever nothing has changed
@@mrghostlyr1162 Viruses thrive off of bad cells. If you have been eating dirty for years, you will be a breeding ground for illness. If you remove the bad cells, virus has nowhere to live. Minimal place to live at best.
@@CRAIGC55 That's not how it works. At least not with corona virus. Corona virus will infect your cells regardless of whether they're "clean" or not.
This is the first time even in my life im watching a pure math video not because of school but because I wanted to... WOW, Michael really is powerful lmao
Michael thank you for all of your Vsauce, Mindfield and Ding videos! The content is some of the most fascinating stuff I've watched on the whole internet. Your method of presentation and your subtle humor makes for a really enjoyable experience.
Plot reveal : Michael is doing maths to avoid being crazy in his asylum
Eh eh eh, no spoilers!
MATH*
@@TheBEST-eg4yd It's called maths you American heathen
@@TheBEST-eg4yd It is called maths
It'S cAlLeD MaFs! Words are words are words. Tyre and aeroplane are weird, though.
Me: Why does this work??
Teacher: bEcAuSe iT DoEs!!
Michael: Weeelll. . .
That's not a teacher, or at least a terrible one
Шнат’s шітһ тһе шеігd теасһег сарітаls ?
@@hafda010 Why are you writing in russian letters?
My favorite part of my Number Theory elective in college was proving the divisibility rules for 3 6 and 9. They seem so not math-y when you learn them as a kid, but the proof is very easy to understand
Michael: "In times like these, _we need to be _*_unified."_*
Okay, how many people immediately said, _"Or _*_do_*_ we?"_
guilty as charged
@@OceanRedux me too!
Ok I'm kinda embarassed to ask this but... so I'm pretty good at english becouse I'm learning it since I was 6 but I still don't understand what "Or do I" meme means
@@antonioocchipinti801 No need to be embarrassed about that! It's something Michael say A LOT in his videos. That's all! 😃 Watch a few more from VSauce and you'll see what we're talking about!
antonio occhipinti the ‘or do i?’ meme uses sarcasm. Sarcasm is a type of humour that becomes funny by doing something unexpected. Like saying (insert random dictator here) did nothing wrong. The joke teller doesn’t think that that person did nothing wrong, but its so unexpected and rude that it becomes funny.
I wish I could divide Michael so I could have a part of him
Who says you cant?
@@davidsphere43
mhm, yes fbi thats the man.
Psycho
Or would you? *que music*
I call dibs on the left foot
“It is so important that we social distance....”
*Five Months Ago*
Ahh yes how quick five months went
isolation has increased the passage of time fivefold
*3months ago*
@@jeggehek6934 and another one, another week down in the books :(
2021
8:31 explains the 3 rule.
11:11 explains the 4 rule.
13:27 explains the 8 rule.
15:40 explains the 7 rule.
1, 2 and 5 are obviously why they work.
5 is always 5 or 0.
2 is all the even number.
And 1 is all the entire numbers that exists.
6 is 2 times 3, so it's obviously why we need to use the 3 rule and see if is even.
(The digital root of a number is sum all its digits and if this new number has more than one digit sum it again until you have only one digit which will be the digital number)
And the digital root of any number multiple of 9 must be 9.
Because 9 is the only number that don't change the result of a digital root.
and mustn't be any number that change the original 9 in the digital root.
For example 729=7+2+9=18=1+8=9
But 3729=3+7+2+9=21=2+1=3
And as you can see here: 73649163=3
73649163 *9* =3. 9 don't change the digital root.
Also I wanna say it's because 9 add 1 ten and put out 1 unit so 9 don't change anything the value.
(Idk if the digital root rule is the correct way of show why it works but I always have that theory and it works so you can explain it in that way)
Thank you!
@@akirefilms5056 your welcome
"They allow us, in this lonely times, to make a bunch of new friends, math friends." --Michael, 2020
At first I thought he was talking about all of us watching this video together. More and more, I am convinced that Michael is talking about the math itself. The math is our new math friends.
Yes
I love how earnest Michael is. Keep making the world a better place
What is earnest?
@@kfdhbdj9224
ear·nest1
/ˈərnəst/
adjective
resulting from or showing sincere and intense conviction.
"an earnest student"
@@drdoof2940 you use reddit by any chance?
I go back and watch this video over and over again simply because the explanations for how it all works is absolutely beautiful, and of course Michael talking about anything always makes it better too
Michael! I though of a way faster method to check divisibility by 7:
1. Take the leading two digits of the number.
2. Divide by 7 and find the remainder.
3. The remainder becomes the new leading term
4. Repeat until you recognize the number as divisible by 7 or not.
E.g.
362,880: Not sure if divisible by 7
36->1
12,880: Not sure
12->5
5,880: Not sure
58->2
280: Pretty sure
28->0
0: Divisible by 7
"in times like these, we need to be unified, but today, were going to divide."
*avengers music starts to play*
vevor jepo thanos wants to chat
10:18 I mean, come on. He just wants us to make memes.
8:25 I was so looking forward for that moment to come, and when it did the song that kicks in when Michael says "or does it?" kicked in my head.
Divisibility in base 6:
*1*
If the number ends in the ones place, then the number is divisible by 1.
(same as 1 in base 10) 1:08
*2*
If the number ends in 0, 2, or 4, then the number is divisible by 2.
(same as 2 in base 10) 1:14
*3*
If the number ends in 0 or 3, then the number is divisible by 3.
(same as 5 in base 10, but replaced by 3) 1:17
*4*
If the sum of the ones place digit and the double of the tens place digit is divisible by 4, then the number is divisible by 4.
(same as 4 in base 10) 3:17
*5*
If the sum of the digits is divisible by 5, then the number is divisible by 5.
(same as 9 in base 10, but replaced by 5) 2:29
Good!
best base
what's the point j/k
Hi, I'm jan Misali, and-
is everything ok here? blink if in need for help
Amateurs- "Number"
Heroes- "Numerical"
Legends- "Number in base 10"
Michael- "Spelling of the number"
(2:28)
Spelling of the number in base (20/5) +(2*3)
Mathematicians - n, such that it is a member of a set R
Well, technically they are digits.
@@tap20 Base 12?
@@jackholmes7003 check again, it equals 10
Just gonna leave this here:
10:18
Bertil Johansson has oooh ooooooh 😫
20:23
Thank you
thank you this has changed my life
Vsauce out of context 4 babeyyy
The way I was always taught to find a multiple of 7 is to double the last digit and subtract it from the rest of the number.
14 = 8 - 1 = 7
49 = 18 - 4 = 14 = 7
798 = 79 - 16 = 63 = 7
"63=7"
Something here isn't adding up...
@@skittybug6937 - 63 = 6 - (3 x 2 = 6) = 0, which technically works.
@@chrisrj9871 r/woosh
don't abuse the equal sign like that
You can do this 7 | 63 "7 divides 63"
or for the other way around, "63 dibisible by 7" i remember using in school three vertical dots like 63 :7 but with this unicode character VERTICAL ELLIPSIS (U+22EE) lookup the code.
or like this 63 % 7 = 0 (modulo operation result )
@@Dm3qXY - It would have been far too long to type what I wanted to say, and I'm just here for fun... I think it makes enough sense once the numbers get smaller.
Nice explanation of the concept which I was looking for a long time, thank you so much for your time and effort.
Oh yeah! Michael is back
OH NO, MICHAEL HAS BEEN LOCKED INSIDE FOR AN INDETERMINATE AMOUNT OF TIME
Flashbacks
chew
I bet Micheal is powerful enough to know what happens when you divide by 0
Hi
Le Rebel Flagship an error message
I've heard when you divide by 0, Chuck Norris appears and does a roundhouse kick.
Le Rebel Flagship it is infinity. You’ll learn about it in calculus when you go over limits
The answer is probably hidden in his beard
Because 200 is evenly divisible by 8, there is an alternate way to check for divisibility by 8.
Given last digits: ...abc, find 2b+c as you did with 4, but if a is odd, add 4, if a is even, ignore it.
If (2b+c +[4, if and only if a is odd]) is divisible by 8 then the original term is divisible by 8 as well.
Michael’s buttery smooth stream of consciousness teaching is absolutely god tier.
When Michael said that the random number is not actually a random number, I felt betrayed.
No number is truly random.
@@Speed001 vsauce theme starts playing
@@Speed001 Or is it?
I could tell by looking at it LOL
@@theneoreformationist It is 9! or factorial
I don't know if 49 is divisible by 7. Let me check that
4 + 9(5) -> 4 + 45
=49
Guess I'll never know
Know your 7 times tables, just like you should know your 8 times tables
o o o o o o o
o o o o o o o
o o o o o o o_
o o o o o o o
o o o o o o o
o o o o o o o_
o o o o o o o
Seven rows and seven columns. Count the o's and then you've got 'em.
Just keep doing the operation like Michael said to. It can take a while. Don’t give up!
Do it the other way: 4 - 2*9 = -14
@@user-en7dx1qp3k that makes no sense at all lol.. you trolled my cranium there hahaha gj.
thank you! Your video is very explanatory. I like your sense of humor
Thank you Michael, this video helped me a lot.
Not exactly a divisibility rule, but:
To check if a number is prime, you only have to check all primes up to its square root.
For example: is 103 prime? It’s square root is between 10 and 11, so check 2, 3, 5, and 7. We know it’s odd and doesn’t end in 5 or 0, and that 1+0+3 =4. The only one left is 7, which we test with the trick in the video: 10 + 5(3) = 25, so 103 is not divisible by 7 and is therefore prime.
why do we check with 2,3,5,7? Sorry I'm not really good lol
@@akkok5059 First why do we only check divisibility with prime numbers? Because non prime numbers can be written as the product of prime numbers. Why is that? Because if your number is divisible by a non prime number, you can divide the factor once more until only prime numbers remain. For example, let's take 20. 20=2×10. But 10 is non prime which means you can divide it. 10=2×5. In the end, 20=2×2×5. You only need to check prime numbers to know if your number is prime. The only prime numbers below 10 are 2, 3, 5 and 7.
@@akkok5059 Secondly, why only check up to the square root? If your number is divisible you can write it as n×N, with n
@@akkok5059 Because the rest of numbers between 1 and 10 are product of primes.
Take the number 103 and check divisibility by 2, then 3. Now we have 4, but if the number is divisible by 4 then it's also divisible by 2 and we checked that already. Next comes 5, then 6 but if the number is divisible by 6 then it's also divisible by 2 and 3 - we checked that already.
Other integers: lmao just check if these digits are divisible
7: R E C U R S I O N
Actually, there are divisibility tests for 7 that are simpler provided you have a fixed number of digits to work with. For example, if I want to work with 3 digits, then any number will expressible as 100a + 10b + c. 98a + 7b will always be divisible by 7, because 98 is divisible by 7, since 98 = 70 + 28, and 28 is divisible by 7. Therefore, one only need check if 2a + 3b + c is divisible by 7 to check if your 3-digit number is divisible by 7. The problem is that this does not generalize as easily to any other number of digits. For example, if you want to check for 4 digits, as in 1000a + 100b + 10c + d, you instead have to check if 6a + 2b + 3c + d is divisible by 7. In other words, the quantity you have to check depends on the number of digits. This does not require recursion, but it trades for having infinitely many rules, one for each number of digits.
@@angelmendez-rivera351 i was gonna say calm down its just a joke but that's actually a really cool point. It's not immediately obvious why 7 causes so many issues
A computer scientist's worst nightmare come alive
@@melovepeas The reason is that 7 is prime, and thus coprime with 10 (it shares no common factors with 10 other than 1). But, you say, it works with multiples of 3 ! And that's because 10 is 1 away from a multiple of three, which is actually a very special thing. Basically, there's no general rule... unless there is one. That is, it only works in special cases and in general you just have to go the recursive route. It's amazing how many things we take for granted about numbers when a lot of properties we think as intrinsic to the numbers themselves are actually dependent on the base being used.
7 is special boi
Michael I just love your enthusiasm for the charity!
These help a lot more than you know in Permutation and Combinations!!
"I'm going to pick a random number"
*it's casually divisible by all numbers from 1 to 10*
@@rmay2215 it's casually 9!
@@alexandreman8601 It'S nOt NiNe ThOuGh
@@UnsIiced it's 9 factorial
"but what is random?" -Michael, 2014
Michael: "let's choose a random number"
Michael: *choses 9!*
i know right
He did it on purpose he winked i think
@@caleblewis8169 Of course, It's not like I didn't know
I knew something fishy was going on.
He writes 8's the same way I do!.. I always though I was weird but now I feel cool 😬
Dwade : also chooses 9
Michael: "...But how do these tricks work?"
Music: "..."
Me: "...Wait, what- nothing??? Wow, I have never felt the absence of the Vsauce music so keenly..."
I remember watching this when it came out. I didn't understand it back then but now after some algebra, and now calculus, This actually makes a lot of sense.
8:26
At this point, I heard the music
me 2
ruclips.net/video/TN25ghkfgQA/видео.html
Michael: now let’s see if it’s divisible by four.
My brain: oh yes, we can half it twice.
Michael: take the first number in the two digit number and double then add it to the second digit.
Me:...
If half the last two digits is even, then it's divisible by 4
Seems way more straightforward
@@KaitouKaiju that doesnt account for numbers like 16. 6/2=3 which isnt even. but as we know 16/2=8, and 8/2=4 so its even
@@dylankrejci9965 It's the last two digits, not the last one. For 16, it'd be 16/2 = 8, which is even, so it's divisible by 4.
Try dividing 426,421,295,739,292,069,436 twice in your head to check. I know it is divisible by four right away thanks to Michaels trick.
@@steffen5121 You don't get it. You only half the last 2 numbers and check if it's even >___>
Awesome, thanks for this!!!
I love your videos Michael Stevens, and I would like to say that I have learnt a lot of fun and exciting things from you.
stop calling him "Michael Stevens" , you're not his mom and he did nothing wrong...
19:22 "Oh! Look at this!" A new meme is born.
Clever.
I like how he went so crazy that he makes these reactions on calculations
just when i thought this channel would never see the light of day again
@@blueshirt1619 we are aware blue shirt. You no longer have to reply with this link anymore. Thank you for your service. -3-
i turned this on while playing a game and didn't notice it was playing, I completely zoned out
the fact that he writes 8 by drawing 2 circles unsettles me
For those of you who forgot the rules as soon as you stopped watching:
2: If the number is even, it can be divided by 2
3:Take all the digits in a given number and sum them up. If the resulting number is divisible by 3, the original number is divisible by 3
4: If the last 2 digits of the number form a number that is divisible by 4, the whole number is. OR. Take the 10s digit and double it, and then add to that the ones digit. If that number is divisible by 4, the original number is as well.
5: If the number ends in 0 or 5, it's divisible by 5
6: If the number is divisible by 3 and is even, it is divisible by 6
7: Take the 1s digit, and multiply it by 5. Then, add to it the remaining numbers as if it were its own number (the whole thing, not each individual digit). If the resulting number is divisible by 7, the original number is as well.
8: Take the hundreds digit, and multiply it by 4. To that, add the tens digit times 2. To that, add the ones digit. If the resulting number is divisible by 8, the original number is divisible by 8.
9: If the sum of all of the digits in a number is divisible by 9, the original number is divisible by 9
REMEMBER: All of these processes can be done multiple times if you are unsure if the resulting number is divisible by the number (1, 2, 3... ,9)
Matthew Riachi thank you soooo much!!
You forgot 1 help
@@xythrr Every number is divisible by 1
@@june349 Not True; Every Integer is divisible by 1, not every number
@@softlysnowing3959 I never said evenly divisible. I just said divisible
i learned a lot of these as a kid and one favorite pastime of mine is to mentally add the digits on license plate numbers to determine whether or not they're divisible by 9 (license plates in my country always have a 4 digit number in them)
I got quite confused by the "4 number digit" thing for a bit so I just wanna let you know you switched those around
Wait, so only 9999 people live in your country? There has to be some other combination of letters added in as well, right?
yee in Latvia we have 4 numbers and 2 letters
@@sharabhojha7895 yeah the format is [one or two letters]-[four numbers]-[two or three letters]
@@user-dt8mf8nt2v right lol
This is exactly what I needed. The finals from last semester were delayed and they'll be soon, and this is a perfect way to remind myself about divisibility rules.
This was great! Thank you
10:18
When she says, my parents aren't home.
🤣👍
0:00 her doorbell after 0.1354 seconds
JS K (*≧m≦*)
@@rjkzk
If "That Guy" can help me out please, I'm trying to learn more about the english language.
Technically that's not more than one second, so should it be "0.1354 second"?
Relevant trivia: The number 2520 is the smallest number that's divisible by 1-10.
Edit: It also has many other interesting properties such as being:
- half of 7! (7 factorial)
- a highly composite number
(if you don't know what that is you may want to watch this video: ruclips.net/video/2JM2oImb9Qg/видео.html)
- a colossally abundant number
(I've tried to find and video or website that explains it in an understandable way but I can't find one)
- a Harshad number (a number that is divisible by the sum of its digits. Ex. 24: 2+4=6, and 24 is divisible by 6)
- the aliquot sum of 1080
(a rare relationship between two numbers where the sum of one of their factors is equal to the second number and the sum of the factors of the second number is equal to the first number. If I didn't explain it well I recommend watching until 1:30 of this video: ruclips.net/video/WtbkBl7ct4I/видео.html)
Thanks for info friend
@@sy7028789 but i think this was a conspiracy theory 😅 isn't it bro?
Math is broken. 2520 single digits should replace 1-10.
I always approve of Numberphile videos. Especially after receiving my piece of pie yesterday :)
@Wouter vanR I prefer Tau over Pi but I kind of feel bad for Pi this year; nearly everyone forgot about Pi day because of the coronavirus
Edit: grammar
i didnt know you made a video about my current math class subject
thank you
The divisibility rules for all powers of 2 stem from the divisibility by 2 rule. The general power of 2 divisibility rule is this:
For any 2^n power divisibility, take the last n digits and sum up this series: 2^(n-1) * 1st digit + 2^(n-2) * 2nd digit ... + nth digit and check if the sum is divisible by 2^n. If you don’t know yet, repeat until you figure out if it’s divisible by 2^n.
I never thought I'd heard Michael say "Dong" again...
Unlike the time he said "Ussie"
Looks like I only knew a fraction of this topic.
Good pun
I don't have much to add here
This made me laugh on *multiple* levels
@Jacob Vachon no matter how hard you try to stop us all, there will always be a remainder...
Divisibility rules of 4, 8, 10, 11, 15, 20, 30 or 50:
4: If the number is divisible by 2 twice.
8: If the number is divisible by 2 thrice.
10: If the number ends in 0, it is.
11: If the sum of the odd positions of the number minus the sum of the even positions of the number is 0 or multiple of 11 (abcd-> (a+c)-(b+d)= 0 or multiple of 11)
15: If the number is divisible by 3 and 5.
20: If the number is divisible by 2 and 10.
30: If the number is divisible by 3 and 10.
50: If the number is divisible by 5 and 10.
when he said "let's pick a completely random number" the number 69 was just written on his face
_All aboard in Michael's online classes!_
D Sauce your name 😂😂😂😂
Kimi no na wa
Bonus divisibility rule: To determine if something can be divided by 11, take off the last 2 digits and add them to the remaining number. Repeat until you have something that you know is divisible by 11.
Ex: 35,365
353 + 65 = 418
4 + 18 = 22 = 2 × 11
Bigger ex: 6,954,035
69,540 + 35 = 69,575
695 + 75 = 770
7 + 70 = 77 = 7 × 11
Explanation: Number abc, last 2 digits are bc.
abc = a × 100 + bc
The operation does:
(abc - bc + (100 × bc)) / 100
Essentially, you're adding 99 × bc to the number, since 99 × is always divisible by 11. However subtracting 1× and adding 100× does the same thing, so you can use that instead.
Mehteh Trollfacer Thank you! Was disappointed that he didn’t show any unknown trick
Simpler method: Add the 1st, 3rd, 5th ........ digits together and the 2nd, 4th, 6th digits together and subtract the two.
If you get a multiple of 11 or 0, it is divisible by 11.
Ex- 35,365
Sum of odd digits = 3 + 3 + 5 = 11
Sum of even digits = 5 + 6 = 11
Difference = 0
Therefore divisible by 11
I have a more interesting trick. Just substract the last digit from the rest of the number. If the result is divisible by 11, then so is the original number.
Ex. 35365
3536-5=3531
353-1=352
35-2=33
3-3=0
0 is divisible by any number except itself, so it's obviously divisible by eleven, and so is 35365
@@sanyalox01 this entire thread is golden, amazing
Beautifully explained!
Love the way you explain
"GIANT PANDEMIC"
Michael: hmmm i haven't uploaded in a long time lets make everyone's day better
Micheal: I'm gonna do what's called a pro gamer move
@sw4gr1d by definition this IS a pandemic. Even if you don't think it's serious, it's still a pandemic because it is worldwide.
I respect Michael so much that I'm getting to bed just to watch him the most comfortable I can be. he deserves all my attention.
B. F. S I M P
Thomas Schmidt michael’s an exception, he’s not a thot
Better than math teachers
@@thomasschmidt4193 reddit moment.
Legit did the same thing. I routinely eat snacks or meals while I watch videos, but opted out of doing that with this one so I could pay attention to it.
How has this channel existed for 5 years and I’m just learning about it now!?!
You know, I just realized something. Ever since Michael's isolation experiment, he has never been the same. Are we going to be ok?
Me: *finally escapes online classes
Michael:
I came here with a Popcorn
I came out with a Mathematics Degree
No one, Duchi: *a* popcorn
only one
Shouldn't you say "went out"?
Also, popcorn with a capital "P", which implies it's either someone's name, or a place's name. You can't carry a place around -or can you?- , so I guess they watched with a friend?
I got halfway through the video and Michael is showing us why these tricks work , I began to realize that this is how I do work in my head instead of writing it all down. this is the way I simplify the work so that I can do it in my head instead of having to work it all out on paper
Michael just taught us Common Core Math in an engaging and understandable way. The Department of Education needs to have him design the curriculum.
As someone with dyscalculia, this is INCREDIBLY helpful. I wish Micheal had been my math teacher! I need to understand HOW math works, otherwise it's too abstract for me. When I was a kid we were expected to just memorize everything by rote with zero explanation, so even as an adult I still struggle with basic multiplication and division. Logic and algebra make more sense to me, so this video is a life saver!
It's Michael, not Micheal
Math should _only_ be about understanding how things work. There should be hardly any memorization at all. It sounds like your difficulty with math had more to do with poor teaching methods.
I feel like my foundation for maths were scrambled by just that. We were always taught to memorize recipes rather than understand how they actually work. I wish I hadn't been taught this way.
@@Cazador1 Whoops, thank you!
What if I told you this video *severely* overcomplicates things?
I suggest reading about the cyclic groups and modular arithmetic. Makes all these results much more basic and really easy to extend to other numbers.