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Published byEdgar Blake Modified over 8 years ago

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EXAMPLE 1 Making a List to Find the GCF An orchestra conductor divides 48 violinists, 24 violists, and 36 cellists into ensembles. Each ensemble has the same number of each instrument. What is the greatest number of ensembles that can be formed? How many violinists, violists, and cellists will be in each ensemble? EXAMPLE 1 Making a List to Find the GCF

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EXAMPLE 1 Making a List to Find the GCF In the orchestra problem, the greatest number of ensembles that can be formed is given by the greatest common factor of 48, 24, and 36. The common factors are 1, 2, 3, 4, 6, and 12. The GCF is 12. ANSWER The greatest common factor of 48, 24, and 36 is 12. So, the greatest number of ensembles that can be formed is 12. Because there are 12 ensembles, divide each instrument group by 12. There will be 4 violinists, 2 violists, and 3 cellists in each ensemble. EXAMPLE 1 Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24 Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36 Making a List to Find the GCF

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GUIDED PRACTICE for Example 1 Find the greatest common factor of the numbers by listing factors. 1. 16, 28 ANSWER 4 2. 60, 96 ANSWER 12 3. 14, 70, 91 ANSWER 7 4. 15, 75, 20 ANSWER 5

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GUIDED PRACTICE ANSWER 8; 4 violinists, 5 violists, 2 cellists for Example 1 What If? What is the greatest number of ensembles that can be formed with 32 violinists, 40 violists, and 16 cellists? How many of each instrument will be in each ensemble? 5.

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