What is the greatest common factor of 8 an 12?

4

Look at the prime decompositions of each

8 = 2*2*2
12 = 2*2*3

Now look at all the terms in common.
They both have at least two 2's.
They share a factor of 4.
What is left after removing 4?
8/4 = 2
12/4 = 3
There is nothing left in common now.
So the greatest common factor is 4.