The Greatest Common Factor (GCF) is the largest positive integer that is a factor of two or more numbers. Look at the examples below to see how to find the Greatest Common Factor.
What is the Greatest Common Factor of 16 and 20?
| What are the factors of 16? | 1 , 2 , 4 , 8 , 16 |
| What are the factors of 20? | 1 , 2 , 4 , 5 , 10 , 20 |
| What factors are common (What are factors of both 16 and 20?) | 1 , 2 , 4 |
| The Greatest Common Factor is …. | 4 |
Here is another example of finding the Greatest Common Factor
What is the Greatest Common Factor of 12 and 42?
| What are the factors of 12 ? | 1 , 2 , 3, 4 , 6 , 12 |
| What are the factors of 42 ? | 1 , 2 , 3 , 6 , 7 , 14 , 21 , 42 |
| What factors are common (What are factors of both 12 and 42 ?) | 1 , 2 , 3 , 6 |
| The Greatest Common Factor is …. | 6 |
Solving problems using the Greatest Common Factor
The example below shows how we can use GCF to solve problems.
Problem: We have three containers. One contains 12 liters of milk, one contains 15 liters of juice and the other 24 liters of water.
We want to empty each container into bottles. The bottles must all be filled and must be the same size.
What is the largest size that the bottles can be?
We need to find the Greatest Common Factor of 12 , 15 , and 24 because that number will be the largest size that the bottles can be.
| What are the factors of 12 ? | 1 , 2 , 3 , 4 , 6 , 12 |
| What are the factors of 15 ? | 1 , 3 , 5 , 15 |
| What are the factors of 24 ? | 1 , 2 , 3 , 4 , 6 , 8 , 12 , 24 |
| What are the factors are common (What are factors of 12 , 15 , and 24 ?) | 1 and 3 |
| The largest the bottles can be is the same as the Greatest Common Factor and is …. | 3 liters |
