Question

How do I find the prime factorization for 180?

I've looked in sundry places for how to find prime factorization, but alas, I continue to follow a confused path.

Answer 1

factor out one prime factor at a time if you have to

180=2*90=

Answer 2

You just simply keep reducing the number in accordance with its factors:
180 = 2(90)
= 2(2)(45)
= 2(2)(3)(15)
= 2(2)(3)(3)(5)