I WISH I knew this factoring trick in 5th grade

[@josephwilles29]

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.

[@vinteachesmath]

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!

[@RanBlakePiano]

Fabulous !

[@vinteachesmath]

Glad you think so!

[@LtSeth242]

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.

[@vinteachesmath]

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!

[@LtSeth242]

@@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.

[@ishakalam3240]

Nice sir

[@vinteachesmath]

Thanks for supporting the channel!

[@danishhraza]

Thankyouu. really helped

[@vinteachesmath]

You're welcome!

[@wxvyonfn7423]

THANK YOU PROF.

[@vinteachesmath]

Happy to help!

[@gentlemandude1]

You're right, this is cool, but WHY does it work? Perhaps that would be a good topic for a future video?

[@vinteachesmath]

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!

[@shauryamittal3011]

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)

[@vinteachesmath]

30 = (2^1)x(3^1)x(5^1), add one to each exponent and multiply: 2x2x2=8

[@148DP]

It definitely does work my friend

[@BHappy2Day]

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

[@asmakhalid2356]

did not understand