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**Greatest common factor**

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**To find the greatest common factor (GCF):**

The greatest common factor (GCF) of two or more numbers is the greatest number that is a factor of these numbers. To find the greatest common factor (GCF): 1. List the factors of each number 2. List the common factors of the numbers 3. Find which common factor is the greatest

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**First Method Find the Greatest Common Factor (GFC) of 12 and 27.**

1. List the factors of each number 1 x 12 = x 27 = 27 2 x 6 = x 9 = 27 3 x 4 = 12 Factors of 12: factors of 27: 1,2,3,4,6,12 1,3,9,27

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**The common factors are : 1, 3 **

3. Find which common factor is the greatest Common factors of 12 and 27: 1, 3 Greatest common factor (GCF) of 12 and 27: 3

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**Find the greatest common factor (GCF) of 16, 28, and 32. **

Study this example: Find the greatest common factor (GCF) of 16, 28, and 32. 1x16 =16 1x28 =28 1x32 =32 2x 8 =16 2x14 =28 2x16 =32 4x 4 =16 4x 7 =28 4x 8 =32 Factors of 16: Factors of 28: Factors of 32: 1,2,4,8, ,2,4,7,14, ,2,4,8,16,32 Common Factors of 16, 28, and 32: 1, 2, 4 Greatest common factor (GCF) of 16, 28, and 32: 4

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**Here you have more examples:**

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. 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.

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**Multiplying Common PRIME Factors**

This is another method to find the greatest common factor. 1. Decompose the numbers in prime factors. 2. select the common factors with the smaller exponents and multiply them.

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Let's take 8 and 32. We decompose the numbers in prime factors. 2 2 1

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**(2 ) = 2 x 2 x 2 = 8 which becomes the greatest common factor.**

2. We select the common factors with the smaller exponents and we multiply them. 2 2 The prime factors of 8 are 2 x 2 x 2. (2 ) 5 the prime factors of 32 are 2 x 2 x 2 x 2 x 2. (2 ) (2 ) has a smaller exponent than (2 ) 3 (2 ) = 2 x 2 x 2 = 8 which becomes the greatest common factor.

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Both methods will help you determine the greatest common factors (GFCs). However, you will need to decide which method you prefer to work with.

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**Class Activity Copy and complete the table. Number Factors**

Common Factors GCF 6 ???? ?? ? 10 18 ?????? 24 ????????

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**List the factors of each number**

List the factors of each number. Then underline the common factors of each pair of numbers. 6 and and 15 3. 4 and and 24 5. 11 and and 12 7. 8 and and 30

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PROBLEM SOLVING Ms. Durkin wants to package 16 math books and 28 science books equally without mixing the books and with none left over. What is the greatest number of books she can put in each package? Mr. Diaz wants to group the 18 girls and 24 boys at the summer camp separately into teams. To be able to match boys with girls during the games , the team sizes have to be the same . What is the greatest team size the boys and girls can form?

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Greatest Common Factor

Greatest Common Factor

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