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Greatest Common Factor

Greatest Common Factor. 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. Find the Greatest Common Factor. Example: 18xy , 36y 2.

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Greatest Common Factor

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  1. Greatest Common Factor

  2. 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.

  3. 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

  4. 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.

  5. Now you try! Find the greatest common factor of the following: Example 1: 12a2b , 90a2b2c GCF = 6a2b Example 2: 15r2 , 35s2 , 70rs GCF = 5

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

  7. Factoring Using the GCF

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

  9. Example: Factor: 12a2 + 16a 1. Factor each term. = 2·2·3·a·a + 2·2·2·2·a · a 2. Factor out the GCF. (3·a + 2·2) = 2 · 2 = 4a (3a + 4) 3. Multiply. You can check by distributing.

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

  11. Now you try! Example 1: 15x + 25x2 = 5x(3 + 5x) Example 2: 12xy + 24xy2 – 30x2y4 = 6xy(2 + 4y – 5xy3)

  12. One last example: Factor: 4x + 12x2 + 16x3 = 2·2·x· + 2·2·3·x·x + 2·2·2·2·x·x·x = 2 (1 + 3·x + 2·2·x·x) · 2 · x = 4x (1 + 3x + 4x2)

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