EXAMPLE 1 Multiple Representations Gardening You are dividing a garden into sections. You have 64...

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

The greatest number of sections that you can have inSOLUTION

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?

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


List all the factors of 64 and 120.

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 23, or 8.


Write the prime factorization of 64 and 120. Then find the product of the common prime factors.

METHOD 2

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 marigoldsand 144 petunias?

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 sectionsyou can have in Example 1 if you have 72 marigoldsand 144 petunias?

EXAMPLE 2 Standardized Test PracticeStandardized Test Practice

EXAMPLE 2

Factors of 16: 1, 2, 4, 8, 16

Standardized Test Practice

SOLUTION

EXAMPLE 2

Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24


Factors of 16: 1, 2, 4, 8, 16

SOLUTION

EXAMPLE 2

Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36


Factors of 16: 1, 2, 4, 8, 16

SOLUTION

Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24

EXAMPLE 2

Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36


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.

EXAMPLE 2

Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36

The correct answer is A.


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.

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

EXAMPLE 3

Find the GCF of the amounts spent by listing the factors.

Ticket Prices

Making a List



SOLUTION

EXAMPLE 3

Factors of 27: 1, 3, 9, 27Find the GCF of the amounts spent by listing the factors.

Ticket Prices

Making a List



SOLUTION

EXAMPLE 3

Factors of 45: 1, 3, 5, 9, 15, 45


Ticket Prices

Making a List



SOLUTION

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


Ticket Prices

Making a List



SOLUTION

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


Ticket Prices

Making a List



SOLUTION

The GCF is 9. The most a ticket could cost is $9.ANSWER

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

GUIDED PRACTICE

The GCF of 14 and 35 is 7.

for Example 2 and 3

Find the GCF of the numbers.

GUIDED PRACTICE

3. 12, 20, 30

for Example 2 and 3


GUIDED PRACTICE

ANSWER

The GCF of 12, 20, and 30 is 2.

3. 12, 20, 30

for Example 2 and 3


GUIDED PRACTICE

4. 24, 48, 72

for Example 2 and 3


GUIDED PRACTICE

ANSWER

The GCF of 24, 48, and 72 is 24.

4. 24, 48, 72

EXAMPLE 1 Multiple Representations Gardening You are dividing a garden into sections. You have 64...

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