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I am asssuming that the numbers are too large for you to simply see them and "know" their GCF.
The easiest way to find the GCF of 2 numbers is the Euclidean method. It is somewhat awkward to explain but once understood, is very easy to use. The idea here is to make the numbers that you are dealing with smaller and smaller so as to simplify the problem.
Suppose you start with the two numbers p and q where p > q. Assume that they are not equal for if p = q, then their GCF is p (or q). The GCF of p and q is the same as the GCF of the smaller number, (say q), and p-q. Repeat this process and keep going until the two numbers are the same.
So, for example, ket us try to find the GCF of 1836 and 1428
GCF(1836, 1428)] = GCF(1428, 1836-1428)
= GCF(1428, 408) = GCF(408, 1428-408)
= GCF(408, 1020) = GCF(408, 1020-408)
= GCF(408, 612) = GCF(408, 612-408)
= GCF(408, 204) = GCF(204, 408-204)
= GCF(204, 204) The two numbers are the same so STOP!
The answer is 204.
It is not a particularly fast method, but it is simple: all you need to now is subtraction.
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