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**GREATEST COMMON FACTOR**

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**GREATEST COMMON FACTOR GCF**

The largest factor two or more numbers have in common. To find the GCF of two or more numbers, you can make a list of all the factors or use prime factorization.

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**Make a list List all of the factors of each number.**

Identify the common factors. The greatest of the common factors is the GCF.

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**24 = 32 = Make a list 32 24 The common factors are: 1, 2, 4, 8**

1, 2, 3, 4,6, 8, 12, 24 1, 2, 4, 8, 16, 32 32 1 x 32 2 x 16 4 x 8 24 1 x 24 2 x 12 3 x 8 4 x 6 The common factors are: 1, 2, 4, 8 The GCF = 8

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**Use Prime Factorization**

Write the prime factorization of each number. Identify all of the common prime factors. The product of the common prime factors is the GCF.

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**Use Prime Factorization**

24 = 32 = 2 2 2 3 24 ^ 6 x 4 ^ ^ 2 x 3 2 x 2 24=2 x 2 x 2 x 3

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**Use Prime Factorization**

24 = 32 = 2 2 2 3 2 2 2 2 2 32 ^ 4 x 8 ^ ^ 2 x 2 2 x 4 ^ 2 x 2 32=2 x 2 x 2 x 2 x 2

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**Use Prime Factorization**

24 = 32 = 2 2 2 3 2 2 2 2 2 2 2 2 x x 4 2 x The GCF = 8

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**Use Prime Factorization**

15 = 45 = 3 5 3 5 3 3 5 x 15 = 3 x 5 15 45 = 3 x 3 x 5 The GCF = 15

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**Use Prime Factorization**

6= 44 = 2 3 2 2 11 2 6 = 2 x 3 44 = 2 x 2 x 11 The GCF = 2

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**Use Prime Factorization**

25 = 56 = 5 5 2 2 2 7 25 = 5 x 5 56 = 2 x 2 x 2 x 7 The GCF = 1

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**Use Prime Factorization**

25 = 56 = 5 5 2 2 2 7 If there are no common prime factors the GCF is one. The GCF = 1

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**Use Prime Factorization**

11 = 22 = 11 11 2 11 11 = prime number 22 = 2 x 11 The GCF = 11

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**Use Prime Factorization**

12 = 18 = 60 = 2 2 3 2 3 3 5 2 2 3 2 3 12 = 2 x 2 x 3 x 18 = 2 x 3 x 3 60 = 2 x 2 x 3 x 5 The GCF = 6

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