1. 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?

2. 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.

3. 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.

4. 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

5. 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?

6. 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

7. EXAMPLE 2
Standardized Test Practice
Standardized Test Practice

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

9. 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

10. 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

11. 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.

12. 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.

13. 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?

14. 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.

15. 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

16. 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

17. 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

18. 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.

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

20. 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.

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

22. 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.

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

24. 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.