Finding the Greatest Common Factor (or GCF) of two or more numbers or algebraic terms is an important process which is explained in this lesson. This process will be used in later lessons on factoring a GCF from an algebraic expression, and on simplifying fractions.

In the first example, we ill find the GCF of two numbers, 15 and 30. Begin by writing down all of the positive factors of each number.

15 (1, 3, 5, 15) 30 (1, 2, 3, 5, 6, 10, 15, 30)

Next, mark all of the factors that both 15 and 30 have in common. In the example below, we marked the numbers by using bold text and highlighting. It is usually more convenient to circle or underline the numbers when working problems out on paper.

15 (1, 3, 5, 15) 30 (1, 2, 3, 5, 6, 10, 15, 30)

The highest number, that both sets of factors have in common is the GCF. In this case, the GCF is 15.

Finding the GCF of two terms that contain variables, like the two terms below, is covered on the next page.

14j2k3 21j