Are you asking for why or just an example of how to use it?

If you are asking for the why of it, basically it's because of the division algorithm, and the fact that products and sums of integers are integers.

For an example, consider 45 and 63:

63 = 1 * 45 + 18

45 = 2 * 18 + 9

18 = 2 * 9 + 0

Thus (45, 63) = 9

-Dan