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?

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? SOLUTION The greatest number of sections that you can have in the garden described above is the GCF of 64 and 120. Two methods for finding the GCF are shown.

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

EXAMPLE 1 Multiple Representations METHOD 2 Write the prime factorization of 64 and 120. Then find the product of the common prime factors. The common prime factors are 2, 2, and 2. The GCF is 23, or 8. The greatest number of sections that you can have is 8. ANSWER

EXAMPLE 1 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?

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? The greatest number of sections that you can have is 72. ANSWER

EXAMPLE 2 Standardized Test Practice Standardized Test Practice

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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