How to Find Greatest Common Factors

Girl looking at math equations on blackboard
Tom Grill/Photographer's Choice RF/Getty Images

Factors are numbers that divide evenly in a number. The greatest common factor of two or more numbers is the largest number that can divide evenly into each of the numbers. Here, you will learn how to find factors and greatest common factors.

You will want to know how to factor numbers when you are trying to simplify fractions.

What You Need


  1. Factors of the number 12: You can evenly divide 12 by 1, 2, 3, 4, 6 and 12.
    Therefore, we can say that 1,2,3,4,6 and 12 are factors of 12.
    We can also say that the greatest or largest factor of 12 is 12.
  2. Factors of 12 and 6: You can evenly divide 12 by 1, 2, 3, 4, 6 and 12. You can evenly divide 6 by 1, 2, 3 and 6. Now, look at both sets of numbers. What is the largest factor of both numbers? 6 is the largest or greatest factor for 12 and 6.
  3. Factors of 8 and 32: You can evenly divide 8 by 1, 2, 4 and 8. You can evenly divide 32 by 1, 2, 4, 8, 16 and 32. Therefore the largest common factor of both numbers is 8.
  4. Multiplying Common Prime Factors: This is another method to find the greatest common factor. Let's take 8 and 32. The prime factors of 8 are 1 x 2 x 2 x 2. Notice that the prime factors of 32 are 1 x 2 x 2 x 2 x 2 x 2. If we multiply the common prime factors of 8 and 32, we get 1 x 2 x 2 x 2 = 8, which becomes the greatest common factor.
  5. Both methods will help you determine the greatest common factors (GFCs), but you will need to decide which method you prefer to work with.
  1. Manipulatives: Use coins or buttons for this concept. Let's say you're trying to find factors of 24. Ask the child to divide the 24 buttons/coins into 2 piles. The child will discover that 12 is a factor. Ask the child how many ways they can evenly divide the coins. Soon they will discover that they can stack the coins into groups of 2, 4, 6, 8, and 12. Always use manipulatives to prove the concept.


  1. Be sure to use coins, buttons, cubes, etc. to prove how finding factors works. It's much easier to learn concretely than abstractly. Once the concept is grasped in a concrete format, it will be much more easily understood abstractly.
  2. This concept requires some ongoing practice. Provide a few sessions with it.