The greatest common factor between any list of numbers is the biggest multiple that they all share. For example, 5, 35 and 50 all share 5 as the biggest common factor, making 5 the greatest common factor.
Now that we have our example and definition out of the way, let's make out the factors.
12: 1 x 12 2 x 6 3 x 4
40: 1 x 40 2 x 20 4 x 10 5 x 8
60: 1 x 60 2 x 30 3 x 20 4 x 15 5 x 12 6 x 10
Now that we have our factors, let's look for the biggest number that they have in common.