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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Example: 30 and 42
Factor them.
2 x 3 x 5 = 30
2 x 3 x 7 = 42
Select the common factors.
2 x 3 = 6, the GCF
The easiest way to tackle this is to look solely at the factors of 6. These are 1, 2, 3 and 6. The next step is to divide 918 by each one in turn to find out what the largest one is which 918 can divide by. In this case, 918 can divide by 6 to give 153. Thus the GCF of 918 and 6 is 6.
The GCF is 5.
The GCF is 4.
You need at least two terms to find a GCF.
You need at least two numbers to find a GCF.