Alexis,

I will demonstrate with different numbers. 
Find the greatest common factor of 24 and and 60.
First find the prime number decomposition of each of the numbers.

24 = 2³ x 3 and 60 = 2² x 3 x 5

Thus 3 divides both 24 and 60, 2 divides both 24 and 60 and also 2² divides both 24 and 60. No other primes or powers of a prime divide both 24 and 60. Thus the largest integer that divides both 24 and 60 is 3 x 2² = 12.

Penny