This document discusses finding the common factors and greatest common factor (GCF) of two numbers. It provides examples of finding the common factors and GCF of 40 and 45 (which is 5), 13 and 15 (which is 1), and 18 and 24 (which is 6). To find the GCF, you list all the factors of each number, identify the common factors, and from those choose the greatest value as the GCF. While there may be multiple common factors, there is only one GCF.

1. Common Factors and Greatest Common Factor Mrs. Young EMC 1

2. What is a factor? Remember that factors are numbers that you multiply together to reach a product Factor x Factor = Product So, factors are numbers that make up a larger number when multiplied together.

3. Find the common factors and the greatest common factor of 40 and 45 Step 1: List all the factors of each number 40: 1, 2, 4, 5, 8, 10, 20, 40 45: 1, 3, 5, 9, 15, 45

4. Step 2: Find the factors that are in both lists 40: 1, 2, 4, 5, 8, 10, 20, 40 45: 1, 3, 5, 9, 15, 45 So, the common factors of 40 and 45 are 1 and 5.

5. Step 3: 40: 1 , 2, 4, 5 , 8, 10, 20, 40 45: 1 , 3, 5 , 9, 15, 45 We know that 1 and 5 are common factors, but the greatest common factor is the common factor with the highest value. Compare the common factors to find the greatest common factor (GCF). So, the greatest common factor (GCF) of 40 and 45 is 5. Note that there will only be ONE greatest common factor, but there may be multiple common factors.

6. Find the common factors and greatest common factor of 13 and 15 Step 1: List all the factors of each number 13: 1, 13 15: 1, 3, 5, 15

7. Step 2: Find the factors that are in both lists 13: 1, 13 15: 1, 3, 5, 15 So, the common factor of 13 and 15 is 1.

8. Step 3: Compare the common factors to find the greatest common factor (GCF). 13: 1 , 13 15: 1 , 3, 5, 15 We know that 1 is the only common factor. So, the greatest common factor (GCF) of 13 and 15 is 1. Note that there will only be ONE greatest common factor, but there may be multiple common factors.

9. Find the common factors and the greatest common factor of 18 and 24 Step 1: List all the factors of each number 18: 1, 2, 3, 6, 9, 18 24: 1, 2, 3, 4, 6, 8, 12, 24

10. Step 2: Find the factors that are in both lists 18: 1, 2, 3, 6, 9, 18 24: 1, 2, 3, 4, 6, 8, 12, 24 So, the common factors of 18 and 24 are 1, 2, 3, and 6

11. Step 3: Compare the common factors to find the greatest common factor (GCF). 18: 1 , 2 , 3 , 6 , 9, 18 24: 1 , 2 , 3 , 4, 6 , 8, 12, 24 We know that 1, 2, 3, and 6 are the common factors, but the greatest common factor is the factor with the greatest value. So, the greatest common factor (GCF) of 18 and 24 is 6. Note that there will only be ONE greatest common factor, but there may be multiple common factors.