Finding the Greatest Common Factor (GCF)

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Presentation transcript:

Finding the Greatest Common Factor (GCF)

Warm Up Find the factors of each number. 28 99 16 68 1,2,4,7,14,28 1,3,9,11,33,99 1,2,4,8,16 1,2,4,17,34,68

Finding the Greatest Common Factor (GCF)

Factors that are the same for two or more numbers are called common factors. The greatest common factor (GCF) for a set of numbers is the greatest factor they have in common.

Example 1: Find the GCF of 12 and 18. List the factors of 12 and 18. The blue factors are all the factors 12 and 18 have in common. 12 – 1, 2, 3, 4, 6, 12 18 – 1, 2, 3, 6, 9, 18 6 is the greatest factor 12 and 18 have in common so the GCF is 6.

Example 2: Find the GCF of 15 and 19. 15 – 1, 15 19 – 1, 19 The GCF is 1.

Example 3: Find the GCF of 10, 25, 40. 10 – 1, 2, 5, 10 25 – 1, 5, 25 40 - 1, 2, 4, 5, 8, 10, 20, 40 The GCF is 5.

Example 4: Find the GCF of 27 and 36 using prime factorization. 9 2 3 2 3 3 3 They both have two 3s in common. 27 = 3 x 3 x 3 36 = 3 x 3 x 2 x 2 The GCF is 3 x 3 = 9.

Practice Find the GCF. 14 and 28 23 and 24 10 and 16 15 and 24 14 1 2

Closure Find the GCF of 64, 72, and 125 1