She is correct. Allow me to illustrate with an illustrative example:
The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36 .
The factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, and 120 .
The common factors are 1, 2, 3, 4, 6, and 12 .
The greatest one is 12 .
36 = 12 x 3
120 = 12 x 10
So (120 - 36) = (12 x 10) - (12 x 3) and that's 12 (10 - 3) .