The general method for finding a prime factorization is to look at the number and start dividing out low numbers that are obvious. I'll show you how I do this for the number 360:
I see that it is an even number, so I can factor out a 2 :
360 = 2 * 180
Now 180 is also even, so I factor out another 2 :
360 = 2 * 2 * 90
Now 90 is also even, so I factor out ANOTHER 2 :
360 = 2 * 2 * 2 * 45
Now I have a 45 to deal with, and that is (3 * 15), so write it that way :
360 = 2 * 2 * 2 * 3 * 15
Now 15 can be factored as (3 * 5), and there are no lower prime factors, so I'm done :
360 = 2 * 2 * 2 * 3 * 3 * 5
and usually instructors like to see it written in exponent form :
360 = (2)^3 * (3)^2 * 5