The prime factorization of a number means to factor out the number into multiples of primes. Let's factor out 45.
45: 1 x 45, 3 x 15, 5 x 9.
Now we have 2 pairs of factors that can be broken down; 3&15, and 5&9. Let's use 5 and 9. 9 can be broken down into 3 x 3. We now have 5 x 3 x 3. This is our factors into primes.