Cool Trick for Factoring Numbers
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- Опубликовано: 16 янв 2015
- Updated video (2021) - • I WISH I knew this fac...
This video teaches students a cool trick for factoring. When listing all the factors a number, students will have trouble knowing if they found ALL the factors. This video teaches students how to find factors of a number and the trick shows students how to check that they found ALL the factors.
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First year college student here, majoring in CS and I slacked off in math throughout school. This channel is helping me catch up so much its a lifesaver
I am happy to help! I am glad to hear that you are challenging yourself with a major like CS. The struggle is definitely worth it!
Same reason why I’m here rn 😂
8 years later...
STILL HELPING PEOPLE!
I am happy to help! I appreciate you supporting my old videos!
After multiple professors and RUclips videos, this is the first technique and explanation I have finally been able to understand and use. Thaaaank you!
you used to be my old math teacher in CSI back in like 2018-2019 you were mad cool and would always tell us to watch the ads I don't think this video had nowhere near this many views at the time. good luck bro and keep it up
Great to hear from you and I appreciate your kind words, Anthony! I enjoyed that time at CSI, I can't believe how fast the years are going. What career path did you choose?!
@@vinteachesmath i graduated with a soc/ant degree but that never was my passion I'm a sales guy so I have always been interested in shoes and have been reselling full time and enjoy making connections with people
Thank You Very Much Sir for putting such informative video. May God Bless you so much happiness and knowledge!!!
That's an amazing trick. I'm going to show this to my son, hopefully it will help him. Thanks for posting it.
Good luck to him and thanks for watching!
@@vinteachesmath oo
@@vinteachesmath good luck your channel will improve
Thank you so much dude because I take a long time listing factors and miss the sneaky ones so this video will benefit me a lot :)
Glad it helped!
Same
So interesting that math works like that sometimes. Best method I've found, thank you!
Thank you so much sir, this was immensely useful for me. Even as a 12th grader taking Maths, I never actually thought there was a way where you could find all factors of a number, but I had to learn. And no video on RUclips was as clear as yours, not only that, but also, very easy to do. Unlike these complex methods on RUclips I found that I honestly could not understand at all or memorize. But this, this is it! Thank you again. (This would've been so useful to learn when I was younger, too. But at least I know now. )
I am very happy to hear that this was so useful! I learned this trick in my last year of college and would have loved to learn this trick earlier!
That is exceptionally cool! I had no idea - thanks for sharing :)
😎
I have always struggled with factoring numbers lol, but this trick has really helped!! Thank you so much :)
Happy to help! I love this trick! This should be shown in every elementary school! I wish I knew it sooner!
Hello Vin,
Currently I'm studying in class 5th and tomorrow is my Maths test so I searched that easiest way to find all factors of a number and after watching this video, I think there will be no doubt in my mind that how to list factors of a number and learnt few new thing from here that exponents and all that thing. It was really helpful no mater this video is uploaded 7 years ago.
Hope the test went well! I appreciate the support, thank you for keeping my old videos relevant!
Best wishes with the rest of your school year.
Thank you for this amazing technique. It's so enlightening. Can you do some videos on LCMs and GCFs, please.
This was a lifesaver. The first video I found that gives me a method that makes sense. Well explained. Thank you.
Glad it helped!
BRILLIANT tutorial. Thanks so much!
I am happy to help! This is one of my favorite math tricks.
This might be late but THANK YOU you’ve made finding factors soooooo much easier
Now this was one amazing and clear video that helped my problems. Thank you for your help.
Glad it helped! Best wishes with the rest of your school year!
Thanks mate! That was really helpful.
Glad it helped! I love this trick, it still blows my mind.
Thanks for the clear lesson.
Glad it was helpful! Thank you for supporting one of my oldest videos. I hope your school year is going well.
VERY COOL TRICK SIR! THANKS FOR SHARING THE TRICK. GOD BLESSES YOU ALWAYS FOR HAVING A KIND-HELPFUL-MIND!
I am glad you appreciate the trick! This needs to be in every elementary and middle school!
Love your accent! Are you from Jersey or PA? Great video it really helped me understand.
NY! I'm glad you liked this video. I wish I knew this technique back in 5th grade
That's fantastic! Thanks a lot for this video!
Glad you liked it!
pretty good tip
love the cool trick!!!
Love this!! But I tried this method with the number 48 and it said 18 but I only got 10 factors? I don't know if something wrong or I messed up..
48 = 2^4 * 3^1.. So do (4+1)*(1+1).. Then there are 10 factors of 48.
wow i've trying to relate it for a long time but with ur help its done so thank u
Glad it helped!
@@vinteachesmath yeah thanks
Thanks you helped me a lot and I mean it
Wonderful explanation, sir. Is there a name for the 'trick' formula, so I can look up how it's derived?
I found this technique in a college combinatorics textbook. It was mentioned somewhat casually but I thought it was very interesting. I remember thinking that this topic should be taught in every elementary school!
Amazing video, thanks a lot!
Glad you liked it! I am very happy that this video did well! I want everyone to know this awesome trick for counting factors.
Its the easiest trick of all, I will use this trick to calculate. THANK YOU VERY MUCH.
Happy to help! I love this trick and I wish I knew it back in grade school!
Very cool... I did get lost on the explanation of “The Trick”
Huge help... who would 'dislike' this!?!?!
Thanks for the upvote! There will always be haters out there...
Well done ,keep going.Your video was very helpful .you are best
Glad it helped!
Thank you after watching this video I clear prime factors concept.
Glad it helped and thanks for supporting one of my original videos!
Thx for this trick it helped me win a math competition
Congratulations on winning the math competition! That is a huge accomplishment! I am glad this trick was useful.
Mr. D, when I tried this trick for factors of 100, my product of prime numbers was 2 squared and 5 squared and my exponents were 2x2x2x2=16. I thought I would be looking for 16 factors of 100. The factors I came up with were not 16 factors but 9 factors and they are listed as 1, 2, 4, 5, 10, 20, 25, 50, 100. Please tell me where I went wrong. Same thing with factoring for the number 27. My exponents indicate 8 factors for 27. What am I doing wrong? Please help.
Wow I tried it now and I got the answer easier than my brother did thanks
This Is sooooo Gonna help me in GRE preparation
Very helpful video!!! 😯
Wow. Really helped me with my exam tomorrow 👌 very helpful, thanks!
thank you so much!
Thats a key right there
THIS IS SOO HELPFUL AND I HAVE A FINAL MATH EXAM COMING UP!!!
How did the final go?!
@@vinteachesmath GREAT!!
The easiest way to _find_ the factors of a larger number, is to complete the prime factorization, then we can simply list all the unique prime factors as factors., then multiply every possible combination of that number. Note that where you have more than one of the same factor, for example, if you have 3 x 3 in your prime factorization, those should be multiplied together, however, if you have 2 x 3 x 3, you don't need to multiply 2 x 3, and the 2 x 3 again. Only unique combinations count.
For 90, as an example, the prime factorization as we know is 2 x 3 x 3 x 5
This therefore means that 2, 3 and 5 must be factors on their own. We can also list 1, obviously.
Now if we take every possible combination of numbers from there, and multiply them we get:
2 x 3 = 6
2 x 5 = 10
3 x 3 = 9
3 x 5 = 15
2 x 3 x 3 = 18
2 x 3 x 5 = 30
3 x 3 x 5 = 45
2 x 3 x 3 x 5 = 90
Then, if we simply sort these out in order, we get: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90
But what if you have a really large number? Well, it's simple. The less prime factors, the less multiplications you have to do, and vice versa
For example, take 30030.
I have chosen this number specifically, because its prime factorization is 2x3x5x7x11x13
Now, since there are no repeated factors, this makes it _even_ easier.
Now firstly, we can obviously list 1, 2, 3, 5, 7, 11, 13, and then 30030 as factors
Now let's multiply every combination:
2 x 3 = 6
2 x 5 = 10
2 x 7 = 14
2 x 11 = 22
2 x 13 = 26
3 x 5 = 15
3 x 7 = 21
3 x 11 = 33
3 x 13 = 39
5 x 7 = 35
5 x 11 = 55
5 x 13 = 65
7 x 11 = 77
7 x 13 = 91
11 x 13 = 143
2 x 3 x 5 = 30
2 x 3 x 7 = 42
2 x 3 x 11 = 66
2 x 3 x 13 = 78
2 x 5 x 7 = 70
2 x 5 x 11 = 110
2 x 5 x 13 = 130
2 x 7 x 11 = 154
2 x 7 x 13 = 182
2 x 11 x 13 = 286
3 x 5 x 7 = 105
3 x 5 x 11 = 165
3 x 5 x 13 = 195
3 x 7 x 11 = 231
3 x 7 x 13 = 273
3 x 11 x 13 = 429
5 x 7 x 11 = 385
5 x 7 x 13 = 455
5 x 11 x 13 = 715
7 x 11 x 13 = 1001
2 x 3 x 5 x 7 = 210
2 x 3 x 5 x 11 = 330
2 x 3 x 5 x 13 = 390
2 x 3 x 7 x 11 = 462
2 x 3 x 7 x 13 = 546
2 x 3 x 11 x 13 = 858
2 x 5 x 7 x 11 = 770
2 x 5 x 7 x 13 = 910
2 x 5 x 11 x 13 = 1430
2 x 7 x 11 x 13 = 2002
3 x 5 x 7 x 11 = 1155
3 x 5 x 7 x 13 = 1365
3 x 5 x 11 x 13 = 2145
3 x 7 x 11 x 13 = 3003
5 x 7 x 11 x 13 = 5005
2 x 3 x 5 x 7 x 11 = 2310
2 x 3 x 5 x 7 x 13 = 2730
2 x 3 x 5 x 11 x 13 = 4290
2 x 3 x 7 x 11 x 13 = 6006
2 x 5 x 7 x 11 x 13 = 10010
3 x 5 x 7 x 11 x 13 = 15015
2 x 3 x 5 x 7 x 11 x 13 = 30030
And so, if we list those in order, we get:
1, 2, 3, 5, 6, 7, 10, 11, 13, 14, 15, 21, 22, 26, 30, 33, 35, 39, 42, 55, 65, 66, 70, 77, 78, 91, 105, 110, 113, 143, 154, 165, 182, 195, 210, 231,273, 286, 330, 385, 390, 429, 455, 462, 546, 715, 770, 858, 910, 1001, 1155, 1365, 1430, 2002, 2145, 2310, 2720, 3003, 4290, 5005, 6006, 10010, 15015, 30030
Of course you can list them as pairs of factors:
1 | 30030
2 | 15015
3 | 10010
5 | 6006
6 | 5005
7 | 4290
10 | 3003
11 | 2720
13 | 2310
14 | 2145
15 | 2002
21 | 1430
22 | 1365
26 | 1155
30 | 1001
33 | 910
35 | 858
39 | 770
42 | 715
55 | 546
65 | 462
66 | 455
70 | 429
77 | 390
78 | 385
91 | 330
105 | 286
110 | 273
113 | 231
143 | 210
154 | 195
162 | 185
I don't know about you but honestly, I don't find it easy at all. Multiplying all possible combinations etc etc like how can I possibly do that, and sometimes there's even a certain order for it, it's just very complicated and it's easy to make mistakes doing it. I like the method shown in this video much more better. But you should do whatever you're comfortable with. What matters is that in the end the result is one, no matter how different a person's methodology might be.
@@_Dreamer_9306
Well, it kind of depends on how many unique prime factors there are.
For example, with a number like 50, you already know 1 and 50 are factors.
Then when you work out the prime factorization, you get 2 x 5 x 5.
So, there's two more factors, 2 and 5.
Now, when you multiply all unique combinations of these prime factors, you get 2 x 5 = 10, and 5 x 5 = 25.
Those are the only ones you need to do.
This gives you the factors of 50: 1, 2, 5, 10, 25 and 50.
However, if you have to do something like 510,510 then even though you'll know that 1 and 510,510 are factors, when you work out the prime factorization, you'll end up with 2 x 3 x 5 x 7 x 11 x 13 x 17.
While this does give you 7 more factors, i.e. 2, 3, 5, 7, 11, 13 and 17, you'll then need to multiply every unique combination of these 7 factors.
In total there are 21 pairs, 35 sets of 3, 35 sets of 4, 21 sets of 5 and 7 sets of 6.
This makes a total of 119 more multiplications. Quite a lot more than just 2.
Thank you!
Very helpful vdo ☺️☺️
LOVE this TRICK!!! I had some GREAT math teachers growing up but can we just clone you across the US bc these math teachers in the NW are dry and boring and they’re trying to reinvent the wheel! Stop making math so difficult for our kids! Just teach to reach! Thank you for this, I’ll pass it along to my boys.
I appreciate the vote of confidence! I hope the boys find it helpful!
Thanks that was so helpful👍
Glad to hear it! Best wishes with the rest of the school year.
Great thank you 🙏
Thank you so much
Thank you so much. Your video is very helpful in avoiding mistakes while factoring.
Amazing and realy helpfull so much !
Glad you think so!
Easy to learn thank u
Nice and clear Good job! 👍
This guy needs an award!
Thanks for the vote of confidence!
@@vinteachesmath my pleasure!
This is a game changer for my 10yr old :)
I am happy to help out the next generation. This trick was casually mentioned in one of my college classes and I remember thinking how I wish I had this back in the day.
I wish your the 10 year old the best with this new trick!
OMG it actually works,my maths exam is tomorrow and i am always confused in finding the factors of 216,Oh My Gosh!!!!, Thank you so so so much 😊😃
Glad it helped! Thanks for supporting my first generation videos!
Very cool tip! I never learned this in school, and now that I'm pandemic-teaching my daughter, this was excellent! (Taught her about exponents too!)
Glad it was helpful! I stumbled across this trick in one of my college classes and thought that this would be great to teach younger students. I wish you and your daughter the best for this school year.
Thanks dude 👍
Thank you 😊 bro 👍 it did really help me
Welcome 😊
@@vinteachesmath will you please share us tricks on cube root and square root
Awesome! Helpful for gmat!
Glad it helped!
Great way to find factors , The trick to find total factors was added bonus....Thank You
I am glad you enjoyed! I wish I had known this trick when I was younger.
best math teach i ever seen bro.
I appreciate the vote of confidence!
Nice and easy method. Thanks
Most welcome!
Hi sir, I was confused when you got 2 out of 5 to the power of 1 if you could reply that would be great. Thanks
Sir salute you, I have my exams on 12th October, please wish me luck🤞🍀
Good luck! I hope your exams go well!
I dont know english even then i understood trick because of your teaching so thanks
Thanks for the tip! I have been searching for an easier way to find all the factors of one such number, and I finally found it!
Glad it helped!
Your math trick partially worked with number 375 the trick part where you add the exponent numbers == 8 so we should have a total of 8 factors, but that's incorrect.
i.e.. 1+1=2 , 3+1=4 then according to your trick you take those two numbers and you multiply
so 2x4 =8 but if you add up all the factors it equals to 6
{1, 3, 5, 75, 125, 375}
I solve the problem but can you help explain what I did wrong or if your trick doesn't work on all numbers thanks much it was cool tho help me find the other factors
ie. 3(5 × 5 × 5) and 5(5 × 5 × 3)
mad props .!
15x25 = 375 is the missing pair!
amazing educator much thanks
Glad you think so!
thanks for the great trick!!
Please help! As stated in another comment, this does not work for #36 (or at least I think it doesnt). The trick tells me that there should be 9 factors when I can find 10. Please explain if and where I am going wrong
Joycinha Borges
The 9 factors of 36 are 1,2,3,4,6,9,12,18, 36
Six shows up twice put we only count it once when we list all the factors. Factors will repeat with all perfect square numbers.
vinteachesmath thank you. Yes I finally worked it out when I counted the facrors and when I counted 6 twice!
Thx so much it helped😊
Glad it helped! I love this trick.
It's really helped me very much 😊☺️😊
Now , my doubt is clear about finding factor of any number 🤗🤗
I am glad the video helped! Thanks for watching.
Incredible tips!! Thanks a lot!
Nice one i like it so much Thank You!!!!!!!!!
I'm glad you like it!
Oml I did not know that trick. That is actually going to help a ton! Thank you!
This helped me a lot thank you!
So helpful! Thank you so much!!
I am glad the video helped! This trick should be taught in every school. It definitely makes it easier to verify that you have found all the factors.
2:02 why should we add the 1, were does it comes from?
You saved my day 🙂Thnq....
Happy to help!
Trick is very good. It gives different approach
I love this trick! Thanks for watching.
That is a VERY cool trick.
Glad you think so! I remember learning this counting factors technique in a college math class and thinking this would be great to learn in the earlier grade levels.
Thanku so much sir.
This was an incredibly helpful trick that helped me immensely whilst taking the accuplacer @ 30 years old.
I hope the accuplacer goes well!
In my school they call it the factor tree method
thanks
Pretty cool that was awsome
Thanks for the support!
thanks. this is one of a few youtube videos I'm using to brush up on my math before taking an assessment test for online college, and it helped me remember how to factor numbers. I think I'm better at it now than I used to be thx to this video! WOOT
I have a test tomorrow, and I’m trying all the videos I can.
I hope your test goes well! Thanks for supporting the channel!
@@vinteachesmath Tysm! I got 100% :)
Thx bro
This is incredible
I love this trick! Thanks for supporting one of my older videos!
It's awesome sir. I appreciate it, how you teach
Wow!!! Awesome
Glad you like it!
Sir, this trick can be apply on all numbers ?😕💭💭
Any whole number greater than 1... Basically, any number that has prime factorization.
Is there a name for the trick? Is there a sound mathematical explanation on why this works? I’m very interested. If someone could tell me that would be great 🙏
Yeay! Awsome
Thanks for the support! Have a great school year!
Extreamly.. Hyperbolically.. Thermodynamically.. Helpful.. 😶😋😁
Thanks so much, you did very well explain...
Shit u did great man you save my valuable tears
LOL, glad it helped!