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**Objectives The student will be able to:**

find the greatest common factor (GCF) for a set of monomials.

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**The Greatest Common Factor (GCF) of 2 or more numbers is**

the largest number that can divide into all of the numbers. 4) Find the GCF of 42 and 60. Write the prime factorization of each number.

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**4) Find the GCF of 42 and 60. = 2 • 3 • 7 60 = 2 • 2 • 3 • 5**

= 2 • • 7 60 = 2 • 2 • 3 • 5 What prime factors do the numbers have in common? Multiply those numbers. The GCF is 2 • 3 = 6 6 is the largest number that can go into 42 and 60!

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What is the GCF of 48 and 64? 2 4 8 16

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**Think Backwards… Find Factors Circle Common Factors**

Group Greatest Factor

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**Step 1: Find the Factors 24 – 1,2,3,4,6,8,12,24**

36 – 1,2,3,4,6,9,12,18,36

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**Step 2: Circle Common Factors**

24 – 1,2,3,4,6,8,12,24 36 – 1,2,3,4,6,9,12,18,36

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**Step 3: Group the Greatest Factor**

24 – 1,2,3,4,6,8,12,24 36 – 1,2,3,4,6,9,12,18,36

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**The Greatest Common Factor of 24 and 36 is…**

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**The Greatest Common Factor of 24 and 36 is…**

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**What is the GCF of 18 and 27? 18 27 Factors of 18: 1, 2, 3, 6, 9, 18**

1 x 18 1 x 27 2 x ? 2 x 9 3 x 9 3 x 6 Factors of 27: 1, 3, 9, 27 4 x ? 5 x ? 4 x ? 6 x ? 5 x ? 7 x ? Common Factors: 1, 3, 9 8 x ? 6 x 3 9 x 3 GCF: 9

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**Ex: Find the GCF(24, 40) Prime Factorizations**

12 2 20 2 6 2 10 2 3 2 5 24 = 2 * 2 * 2 * 3 40 = 2 * 2 * 2 * 5

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**Ex: Find the GCF(32, 51) Prime Factorization:**

16 3 17 2 8 2 4 51 = 3 * 17 2 2 32 = 2 * 2 * 2 * 2 * 2

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**Ex: Find the GCF(102, 84) Prime Factorization:**

51 2 42 3 17 2 21 3 7 32 = 2 * 3 * 17 51 = 2 * 2 *3 * 7

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