One way is to create a factor tree for each number. Then see which factors they have in common.
Example:
12 30
^ ^
2 6 3 10
^ ^
2 3 2 5
The factors are the underlined numbers above:
12: 2 x 2 x 3
30: 2 x 3 x 5
The common factors are: 2, 3, and 6 why 6? because 2 x 3 = 6
The greatest common factor is: 6
