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Using the GCF to Solve Problems

ANSWER. The most groups that can be formed is 12 . Dividing the number of each type of musician by 12 , you find each group will have 4 violinists, 2 violists, and 3 cellists. Example 2. Using the GCF to Solve Problems.

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Using the GCF to Solve Problems

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  1. ANSWER The most groups that can be formed is 12. Dividing the number of each type of musician by 12, you find each group will have 4 violinists, 2 violists, and 3 cellists. Example 2 Using the GCF to Solve Problems In the orchestra problem on page 10, the most groups that can be formed is given by the greatest common factor of 48, 24, and 36. Factors of 48: Factors of 24: Factors of 36: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 1, 2, 3, 4, 6, 8, 12, 24 1, 2, 3, 4, 6, 9, 12, 18, 36 The common factors are 1, 2, 3, 4, 6, and 12. The GCF is 12.

  2. ´ ´ ´ ´ 180 = 2 2 3 3 5 ´ ´ ´ 126 = 2 3 3 7 From the factor trees you see the common factors are 2, 3, and 3. So, the GCF is . ANSWER ´ 32 = 18 2 Example 3 Using Prime Factorization to Find the GCF Find the greatest common factor of the numbers using prime factorization. a.180, 126

  3. Find the greatest common factor of the numbers using prime factorization. b.28, 45 ´ ´ 28 = 2 2 7 ´ ´ 45 = 3 3 5 The factor trees show no common prime factors, so the GCF is 1. ANSWER Example 3 Using Prime Factorization to Find the GCF

  4. Guided Practice ANSWER 8 groups; 4 violinists, 5 violists, 2 cellists for Examples 2 and 3 5. WHAT IF? What is the most groups possible with 32 violinists, 40 violists, and 16 cellists? How many of each type of musician will be in each group?

  5. Guided Practice Find the GCF of the numbers using prime factorization. 6. 90, 150 30 ANSWER 12 ANSWER 24 ANSWER 1 ANSWER for Examples 2 and 3 7. 84, 216 8. 120, 192 9. 49, 144

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