I’m confused on how to know which factors to choose when breaking down numbers? For example, I am currently reviewing how to find the GCF using primes. The numbers given were 360 and 780. For 360 I chose to break it down into 36 and 100 and factor it out from there. The numbers used in the example were 6 and 60. For 780, I used 78 and 10, but the example used 20 and 39. This caused me to get an incorrect answer, but how do I know which factors I should be using. I am so confused.

Thanks!!

Break it down as far as possible till you get prime numbers. Otherwise, it doesn’t matter.

BTW: 36 \times 100 = 3600, not 360

Oops, that was definitely part of the problem. I know I need to break it down into all primes, but how do I know to choose (for 360) 6 and 60 vs 36 and 10? That’s what I’m stuck on.

Both are fine - as you keep on decomposing the numbers, you should end up with the same set of prime factors.

For example,

- 6 = 2 \times 3
- 60 = 2 \times 30 = 2 \times (2 \times 3 \times 5) = 2^2 \times 3 \times 5

Hence,

360 = (2 \times 3) \times (2^2 \times 3 \times 5)

360 = 2^3 \times 3^2 \times 5

Can you show the same if you take 36 and 10 instead?