First you must be pretty confident with at least 9 or so primes to get used to it, so you should at least memorized, 2,3,5,7,11,13,17,19,23,29...
Now take any number, say 104, you would start at the smallest prime and work upwards dividing by primes....
104/2=52/2=26/2=13 which is prime so the factorization is the list of those divisions that you made..in this case
104=2*2*2*13 which can be also expressed as
104=2^3*13
