6th Grade Math: How to Find the Greatest Common Factor

Steps for Finding the Greatest Common Factor

The greatest common factor, or GCF, of a set of numbers is the largest number that every number in that set can be divided evenly by. Your teacher will usually ask you to find the GCF of just two numbers, but sometimes you'll find it for three or more numbers. No matter how many numbers you're finding the GCF for, the steps are always the same.

List the Factors for Each Number in Your Set

First, write down a list of the factors for each number you're given. A number's factors are all of the numbers that it can be divided evenly by. For example, let's say you're finding the GCF of nine and 18. You would list all of the factors of nine, which are one, three and nine. Then you'd list the factors of 18, which are one, two, three, six, nine and 18.

Compare Your Lists of Factors

Next, compare the lists of factors you made for each number. To find the GCF, look for the biggest number that is on both lists.

Let's look at the example of nine and 18 again. Earlier, we listed all of their factors. Now, we need to find the largest number that is a factor of both of them. One, three and nine are all factors of both nine and 18. The GCF of nine and 18 is nine because it is the largest number on this list.

Practice Finding the GCF

Below are some examples to help you practice finding the GCF. In each example, we'll follow these steps:

1. List the factors for each number in the set.
2. Compare the lists to see which numbers are on all of them.
3. Find the largest number that appears on all lists. That number is the GCF.

Example 1: Find the GCF of 24 and 32

First, we'll list the factors for each number. The factors of 24 are one, two, three, four, six, eight, 12 and 24. For 32, the factors are one, two, four, eight, 16 and 32.

Next, we'll find the largest number that's on both lists of factors. One, two, four and eight are all factors of both 24 and 32. However, eight is the largest number on both lists, so it is the GCF.

Example 2: Find the GCF of 15 and 17

We'll begin by listing all the factors of 15 and 17. One, three, five and 15 are the factors of 15. The number 17 is prime, so it only has two factors: one and 17. Next, we'll compare the two lists. The only number that appears on both lists of factors is one, so it is the GCF of 15 and 17.

Example 3: Find the GCF of 12, 15 and 18

Remember that your teacher might ask you to find the GCF of three or more numbers. Here's how you figure it out:

First, list the factors of each number, just like you did before. Twelve's factors are one, two, three, four, six and 12. The number 15 has one, three, five and 15 as its factors. Finally, the factors of 18 are one, two, three, six, nine and 18.

Now, instead of comparing just two lists, you'll have to compare three. The numbers one and three are on all three lists, so they are the common factors of 12, 15 and 18. Since three is larger than one, three is the GCF of this set of numbers.

Tip: Some numbers, like two and six, appeared on two of the three lists, but that's not good enough. To be the greatest common factor, a number must be a factor of every number in the set that you're given, and it must be largest of all of the numbers that fit this description.