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.