While there are many ways to find the greatest common factor between two or more numbers, the list-and-compare method is the simplest. You just need to know that **a factor is one of the two numbers you multiply together** to get a product. Prime numbers have only two factors: 1 and the number itself. Composite numbers have more factors. Three is a prime number; you can only multiply 1 and 3 to get 3 as the product. By contrast, 12 is a composite number with factors of: 1 and 12; 2 and 6; and 3 and 4.

## Listing the Factors

Taking one number at a time, list all of the factors that produce the number. For example, to find the greatest common factor of **10 and 25**, list the factors of each. The factors of **10** are **1, 2, 5** and **10**; the factors of **25** are **1, 5** and **25**.

## Finding the Greatest Common Factor

Circle all of the factors that appear in both lists. These are **the common factors**. To make it easier to see the common factors, use a different color pen or pencil than the one you used to list the factors. In the previous example, you would circle **1** and **5**, the factors both numbers have in common. Now, look at the circled factors and find the greatest common factor -- which is **5** for this example.