factors of 30:
1, 30, 2, 15, 3, 10, 6, 5
For it to be the GCF(greatest common factor), the number has to be a factor of ALL of the other numbers in the question. That means that the GCF is in the factors of 30. Of the factors of 30, these are the ones that are also factors of 48:
1, 2, 3, 6
Now we do the same thing with 60:
1, 2, 3, 6
of the final 4 numbers, 6 is the greatest, making it the GCF of 30, 48, and 60.