Introduction

Greatest Common Factors

In math, factors are the numbers we multiply to get a product, and the greatest common factor is the largest factor that two or more numbers have in common. We often call it the GCF, and we use it when simplifying and reducing fractions. Let’s look at a few examples.

10 and 20

The directions say “Find the greatest common factor of 10 and 20.” Let’s find the greatest common factor of 10 and 20. To find the Greatest Common Factor or GCF, we list the multiples of each number. To do this, we set up a table to stay neat and organized. We list the factors and keep them in numerical order. The factors of 10 are 1 and 10; we will put the 10 over here to make room for smaller factors. 2 and 5, and nothing else. The factors of 10 are 1, 2, 5, and 10. Now let’s move to 20. The factors of 20 are 1 and 20, 2 and 10, 4 and 5, and nothing else. The factors of 20 are 1, 2, 4, 5, 10, 20.

Now we look at the list of factors and determine which factors they have in common. They share 1; one is a shared factor of all numbers. They share 2, they share 5, and they share 10. The greatest of the factors that they share is 10, so the GCF is 10. The greatest common factor of 10 and 20 is 10.

16 and 24

The directions say “Find the GCF of 16 and 24.” We set up a table and we list the factors. The factors of 16 are 1 and 16, 2 and 8, 4 and 4. We only list 4 once. The factors of 16 are 1, 2, 4, 8, 16. Now let’s move to 24. The factors of 24 are 1 and 24, 2 and 12, 3 and 8, 4 and 6, and nothing else. The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24. The factors they share are 1, 2, 4, and 8, and that’s it. The greatest of the factors they share is 8. The greatest common factor of 16 and 24 is 8.

9 and 15

The directions say “Find the greatest common factor of 9 and 15.” The factors of 9 are 1 and 9, 3 and 3; we only put 3 once. The factors of 9 are 1, 3, and 9. The factors of 15 are 1 and 15, 3 and 5, and nothing else. The factors of 15 are 1, 3, 5, and 15. The factors they share are 1 and 3. The greatest factor they share is 3. The GCF of 9 and 15 is 3.