Another way to find GCF is by the euclidean algorithm. Even though the name sounds intimidating, it is probably the easiest method, especially if the numbers are large.
The method consists of calculating the difference of the two given numbers. Then among the two numbers and the difference, repeat with the two smaller numbers until the difference is zero. The smallest surviving number is then the GCF.
As an example for 64 and 28.
64-28=36. Choose the smaller two numbers and repeat
36-28=8 Choose the smaller two numbers and repeat
28-8=20 Choose the smaller two numbers and repeat
20-8=12 Choose the smaller two numbers and repeat
12-8=4 Choose the smaller two numbers and repeat
8-2*4=0 therefore 4 is the GCF.
As a short-cut, when the larger number is much larger than the smaller, we can subtract a multiple of the smaller number. Example again using 64 and 28.
64-28=36
36-28=8
28-3*8=28-24=4
8-2*4=0 Therefore 4 is the GCF of 64 and 28.
As a more adventurous example, let's find the GCF of 3888 and 3774.
3888-3774=114
3774-30*114=354
354-3*114=12
12-8*12=6
12-2*6=0 Therefore 6 is the GCF of 3888 and 3774.