I always had learned we learn to checking factors start at 1 and we write factor pairs and work our way inward. We stop at or near integer square root of number to stop. This is great. Thank you.
That is the same way I learned this way back in the day as well. I wish I knew this trick back then so I would've known for sure that I found all the factors. Thanks for the support!
Love this video. Much appreciated! Trying to incorporate this to teach it to my students so they can have a guide to finding factors, but can you tell me why this works? I don't remember the why behind it, only remember the how it works.
This trick is an application of the multiplication principle from combinatorics. This is the same concept as "Vin has 4 different T-shirts and 3 different pairs of pants. How many outfits can he make? Ans: 4*3 = 12" For this number trick, let's use 12 as an example. 12 = 2^2 * 3^1, so there are (2+1)(1+1) = 6 factors of 12. Any factor is built up of a combination of a 2 or a 3 (similar to a t-shirt and pants from the last example). However, for one of the factors involving 2, we could use 2^0, 2^1 or 2^2; that exponent 0 case adds one extra potential choice for each factor, that is why we add 1. For 3, there is 3^0 or 3^1, so there are two choices for the factor involving 3. The first factor 1, should be thought of as 1 = 2^0 3^0, and 12 can thought of as 12 = 2^2 3^1. This is a tricky concept to type, but I hope this explanation helps!
@@vinteachesmath It's perfect. Thank you! That's what I thought the reasoning was, and I tried justifying it to myself, but kept thinking that 0 isn't adding anything.
Awesome idea! I will add this to the queue! The short answer before the video is the multiplication principle. But this deserves its own video for sure!
give the numbers that have no exponents the exponent of 1 (cause a number to the power of 1 will still equal that number) then follow the steps as per the video. It works
I always had learned we learn to checking factors start at 1 and we write factor pairs and work our way inward. We stop at or near integer square root of number to stop. This is great. Thank you.
That is the same way I learned this way back in the day as well. I wish I knew this trick back then so I would've known for sure that I found all the factors.
Thanks for the support!
Fabulous !
Glad you think so!
Nice sir
Thanks for supporting the channel!
THANK YOU PROF.
Happy to help!
Thankyouu. really helped
You're welcome!
Love this video. Much appreciated! Trying to incorporate this to teach it to my students so they can have a guide to finding factors, but can you tell me why this works? I don't remember the why behind it, only remember the how it works.
This trick is an application of the multiplication principle from combinatorics. This is the same concept as "Vin has 4 different T-shirts and 3 different pairs of pants. How many outfits can he make? Ans: 4*3 = 12"
For this number trick, let's use 12 as an example. 12 = 2^2 * 3^1, so there are (2+1)(1+1) = 6 factors of 12. Any factor is built up of a combination of a 2 or a 3 (similar to a t-shirt and pants from the last example). However, for one of the factors involving 2, we could use 2^0, 2^1 or 2^2; that exponent 0 case adds one extra potential choice for each factor, that is why we add 1. For 3, there is 3^0 or 3^1, so there are two choices for the factor involving 3.
The first factor 1, should be thought of as 1 = 2^0 3^0, and 12 can thought of as 12 = 2^2 3^1.
This is a tricky concept to type, but I hope this explanation helps!
@@vinteachesmath It's perfect. Thank you! That's what I thought the reasoning was, and I tried justifying it to myself, but kept thinking that 0 isn't adding anything.
You're right, this is cool, but WHY does it work? Perhaps that would be a good topic for a future video?
Awesome idea! I will add this to the queue! The short answer before the video is the multiplication principle. But this deserves its own video for sure!
this trick doesn't work on 30(this trick says there are total 6 factors of 30 but there are actually 8 factors (1x30,2x15,3x10, 5x6)
30 = (2^1)x(3^1)x(5^1), add one to each exponent and multiply:
2x2x2=8
It definitely does work my friend
give the numbers that have no exponents the exponent of 1 (cause a number to the power of 1 will still equal that number) then follow the steps as per the video. It works
did not understand