310 = 31 * 10 = 31 * 5 * 2
120 = 12 * 10 = 3 * 4 * 2 * 5 = 3 * 2 * 2 * 2 * 5
252 = 4 * 63 = 2 * 2 * 7 * 9 = 2 * 2 * 7 * 3 * 3
I'm going ro rearrange the factors and use spacing to make the GCF more obvious:
310 = 2 * 5 * 31
120 = 2 * 2 * 2 * 3 * 5
252 = 2 * 2 * 3 * 3 * 7
From this view it should be clear that there is only one factor common to all three numbers: 2. The GCF is 2.