126 = 2 x 3 x 3 x 7
264 = 2 x 2 x 2 x 3 x 11
The greatest common factor is the largest number that divides evenly into both; you can use only those factors which are in each, there is only one 2 in each, one 3 in each, and the 7 and the 11 isn't in both, so you ignore them.
It will have one 2 and one 3: 2 x 3 = 6
126 = 2 x 3 x 3 x 7
264 = 2 x 2 x 2 x 3 x 11
The greatest common factor is the largest number that divides evenly into both; you can use only those factors which are in each, there is only one 2 in each, one 3 in each, and the 7 and the 11 isn't in both, so you ignore them.
It will have one 2 and one 3: 2 x 3 = 6