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EXAMPLE 1 Multiple Representations Gardening You are dividing a garden into sections. You have 64 marigolds and 120 petunias. You want each section to have the same number of each type of flower and use all the flowers. At most, how many sections can you have?

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EXAMPLE 1 The greatest number of sections that you can have in SOLUTION Multiple Representations Two methods for finding the GCF are shown. the garden described above is the GCF of 64 and 120. Gardening You are dividing a garden into sections. You have 64 marigolds and 120 petunias. You want each section to have the same number of each type of flower and use all the flowers. At most, how many sections can you have?

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EXAMPLE 1 The common factors are 1, 2, 4, and 8. The GCF is 8. Factors of 120 : 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120 Factors of 64 : 1, 2, 4, 8, 16, 32, 64 METHOD 1 Multiple Representations List all the factors of 64 and 120.

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EXAMPLE 1 The greatest number of sections that you can have is 8. ANSWER The common prime factors are 2, 2, and 2. The GCF is 2 3, or 8. Multiple Representations Write the prime factorization of 64 and 120. Then find the product of the common prime factors. METHOD 2

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EXAMPLE 1 1. What If? What is the greatest number of sections GUIDED PRACTICE for Example 1 you can have in Example 1 if you have 72 marigolds and 144 petunias?

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The greatest number of sections that you can have is 72. ANSWER GUIDED PRACTICE for Example 1 1. What If? What is the greatest number of sections you can have in Example 1 if you have 72 marigolds and 144 petunias?

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EXAMPLE 2 Standardized Test Practice

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EXAMPLE 2 Factors of 16 : 1, 2, 4, 8, 16 Standardized Test Practice SOLUTION

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EXAMPLE 2 Factors of 24 : 1, 2, 3, 4, 6, 8, 12, 24 Standardized Test Practice Factors of 16 : 1, 2, 4, 8, 16 SOLUTION

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EXAMPLE 2 Factors of 36 : 1, 2, 3, 4, 6, 9, 12, 18, 36 Standardized Test Practice Factors of 16 : 1, 2, 4, 8, 16 SOLUTION Factors of 24 : 1, 2, 3, 4, 6, 8, 12, 24

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EXAMPLE 2 Factors of 36 : 1, 2, 3, 4, 6, 9, 12, 18, 36 Standardized Test Practice Factors of 16 : 1, 2, 4, 8, 16 SOLUTION Factors of 24 : 1, 2, 3, 4, 6, 8, 12, 24 ANSWER The GCF of 16, 24, and 36 is 4.

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EXAMPLE 2 Factors of 36 : 1, 2, 3, 4, 6, 9, 12, 18, 36 The correct answer is A. Standardized Test Practice Factors of 16 : 1, 2, 4, 8, 16 SOLUTION Factors of 24 : 1, 2, 3, 4, 6, 8, 12, 24 ANSWER The GCF of 16, 24, and 36 is 4.

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EXAMPLE 3 Ticket Prices Making a List Three groups will pay $27, $45, and $72 to take the Cave same price. What is the most a ticket could cost? of the Winds tour of Niagara Falls. Each ticket is the

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EXAMPLE 3 Find the GCF of the amounts spent by listing the factors. Ticket Prices Making a List Three groups will pay $27, $45, and $72 to take the Cave same price. What is the most a ticket could cost? of the Winds tour of Niagara Falls. Each ticket is the SOLUTION

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EXAMPLE 3 Factors of 27 : 1, 3, 9, 27 Find the GCF of the amounts spent by listing the factors. Ticket Prices Making a List Three groups will pay $27, $45, and $72 to take the Cave same price. What is the most a ticket could cost? of the Winds tour of Niagara Falls. Each ticket is the SOLUTION

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EXAMPLE 3 Factors of 45 : 1, 3, 5, 9, 15, 45 Factors of 27 : 1, 3, 9, 27 Find the GCF of the amounts spent by listing the factors. Ticket Prices Making a List Three groups will pay $27, $45, and $72 to take the Cave same price. What is the most a ticket could cost? of the Winds tour of Niagara Falls. Each ticket is the SOLUTION

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EXAMPLE 3 Factors of 72 : 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72 Factors of 45 : 1, 3, 5, 9, 15, 45 Factors of 27 : 1, 3, 9, 27 Find the GCF of the amounts spent by listing the factors. Ticket Prices Making a List Three groups will pay $27, $45, and $72 to take the Cave same price. What is the most a ticket could cost? of the Winds tour of Niagara Falls. Each ticket is the SOLUTION

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EXAMPLE 3 Factors of 72 : 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72 Factors of 45 : 1, 3, 5, 9, 15, 45 Factors of 27 : 1, 3, 9, 27 Find the GCF of the amounts spent by listing the factors. Ticket Prices Making a List Three groups will pay $27, $45, and $72 to take the Cave same price. What is the most a ticket could cost? of the Winds tour of Niagara Falls. Each ticket is the SOLUTION The GCF is 9. The most a ticket could cost is $9.ANSWER

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for Example 2 and 3 Find the GCF of the numbers , 35 GUIDED PRACTICE

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for Example 2 and 3 Find the GCF of the numbers , 35 ANSWER GUIDED PRACTICE The GCF of 14 and 35 is 7.

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for Example 2 and 3 Find the GCF of the numbers. GUIDED PRACTICE 3. 12, 20, 30

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for Example 2 and 3 Find the GCF of the numbers. GUIDED PRACTICE ANSWER The GCF of 12, 20, and 30 is , 20, 30

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for Example 2 and 3 Find the GCF of the numbers. GUIDED PRACTICE 4. 24, 48, 72

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for Example 2 and 3 Find the GCF of the numbers. GUIDED PRACTICE ANSWER The GCF of 24, 48, and 72 is , 48, 72

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