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**Greatest Common Factor**

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**Greatest Common Factor**

The greatest common factor (GCF) is the product of the prime factors both numbers have in common. Or It is the largest number that is a factor of all original numbers.

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**Find the Greatest Common Factor**

Example: 18xy , 36y2 18xy = 2 · 3 · 3 · x · y 36y2 = 2 · 2 · 3 · 3 · y · y GCF = 2 · 3 · 3 · y = 18y

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**Tips for finding the GCF**

Find the prime factorization of each item. Circle what is common. Multiply together what is common to get the GCF.

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**Now you try! Find the greatest common factor of the following:**

Example 1: 12a2b , 90a2b2c GCF = 6a2b Example 2: 15r2 , 35s2 , 70rs GCF = 5

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Last Example What is the greatest common factor of 15ab and 16c?

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**Factoring Using the GCF**

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Factoring “Undoing” distribution Finding factors that, when multiplied, form the original polynomial

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**Example: Factor: 12a2 + 16a = 2·2·3·a·a + 2·2·2·2·a = 2 · 2 · a**

1. Factor each term. = 2·2·3·a·a + 2·2·2·2·a 2. Factor out the GCF. = 2 · 2 · a (3·a + 2·2) = 4a (3a + 4) 3. Multiply. You can check by distributing.

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Example: Factor: 18cd2 + 12c2d + 9cd = 2·3·3·c·d·d + 2·2·3·c·c·d + 3·3·c·d = 3 · c · d (2·3·d + 2·2·c + 3) = 3cd (6d + 4c + 3)

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**Now you try! Example 1: 15x + 25x2 Example 2: 12xy + 24xy2 – 30x2y4**

= 6xy(2 + 4y – 5xy3)

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**One last example: Factor: 4x + 12x2 + 16x3**

= 2·2·x· + 2·2·3·x·x + 2·2·2·2·x·x·x = 2 · 2 · x (1 + 3·x + 2·2·x·x) = 4x (1 + 3x + 4x2)

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