Factoring and Multiples

The prime factorization of 60 is 2 x 2 x 3 x 5 or 2^2 x 3 x 5

2 x 2 x 3 x 5 = 60
The prime factorization is the set of prime numbers (including any repeats) that multiplied together give 60.

To start, break it down into something more manageable. You know that 60=6 x 10.
Neither of them is prime, so you have to keep going. 6=2x3. 2 and 3 are both primes, so that's finished. Now do the same for 10. The the prime factorization of 60 is the prime factorization of 6 and 10, again, including any repeats.
2 x 2 x 3 x 5