1. I CAN find the greatest common factor (GCF) of a set of numbers
I CAN find the greatest common factor (GCF) of a set of numbers. I CAN solve word problems involving GCF.

2. Vocabulary
greatest common factor (GCF)‏

3. Factors shared by two or more whole numbers are called common factors
Factors shared by two or more whole numbers are called common factors. The largest of the common factors is called the greatest common factor, or GCF.
Factors of 24:
Factors of 36:
Common factors: 1, 2, 3, 4, 6, 8,
12, 24 1, 2, 3, 4, 6, 9,
12,
18, 36
1, 2, 3, 4, 6, 12
The greatest common factor (GCF) of 24 and 36 is 12.
Example 1 shows three different methods for finding the GCF.

4. Example 1: Finding the GCF
Find the GCF of the set of numbers.
A. 28 and 42
Method 1: List the factors.
factors of 28:
factors of 42:
List all the factors. 1, 2, 4, 7,
14, 28 1, 2, 3, 6, 7,
14,
21, 42
Circle the GCF.
The GCF of 28 and 42 is 14.

5. Example 1: Finding the GCF
Find the GCF of the set of numbers.
B. 18, 30, and 24
Method 2: Use the prime factorization.
18 =
30 =
24 = 2 • 3 • 3
Write the prime factorization of each number. 2 • 3 • 5 2 • 3 • 2 • 2
Find the common prime factors.
Find the prime factors common to all the numbers.
2 • 3 = 6
The GCF of 18, 30, and 24 is 6.

6. Example 1: Finding the GCF
Find the GCF of the set of numbers.
C. 45, 18, and 27
Method 3: Use a ladder diagram. 3
Begin with a factor that divides into each number. Keep dividing until the three have no common factors. 3
Find the product of the numbers you divided by.
3 • 3 = 9
The GCF of 45, 18, and 27 is 9.

7. Find the GCF of the set of numbers.
You Try! Example 1
Find the GCF of the set of numbers.
A. 18 and 36
Method 1: List the factors.
factors of 18:
factors of 36:
List all the factors. 1, 2, 3, 6, 9, 18 1, 2, 3, 4, 6, 9,
12,
18, 36
Circle the GCF.
The GCF of 18 and 36 is 18.

8. Find the GCF of the set of numbers.
You Try! Example 1
Find the GCF of the set of numbers.
B. 10, 20, and 30
Method 2: Use the prime factorization.
10 =
20 =
30 = 2 • 5
Write the prime factorization of each number. 2 • 5 • 2 2 • 5 • 3
Find the common prime factors.
Find the prime factors common to all the numbers.
2 • 5 = 10
The GCF of 10, 20, and 30 is 10.

9. Find the GCF of the set of numbers.
You Try! Example 1
Find the GCF of the set of numbers.
C. 40, 16, and 24
Method 3: Use a ladder diagram. 2
Begin with a factor that divides into each number. Keep dividing until the three have no common factors. 2 2
Find the product of the numbers you divided by.
2 • 2 • 2 = 8
The GCF of 40, 16, and 24 is 8.

10. Example 2: Problem Solving Application
Jenna has 16 red flowers and 24 yellow flowers. She wants to make bouquets with the same number of each color flower in each bouquet. What is the greatest number of bouquets she can make?
The greatest number of bouquets Jenna can make is 8.

11. You Try! Example 2
Peter has 18 oranges and 27 pears. He wants to make fruit baskets with the same number of each fruit in each basket. What is the greatest number of fruit baskets he can make?
The greatest number of baskets Peter can make is 9.

12. Reflection
CAN YOU find the GCF of a set of numbers? CAN YOU solve problems involving GCF?

13. Lesson Quiz: Part I
Find the greatest common factor of each set of numbers.
1. 18 and 30
2. 20 and 35
3. 8, 28, 52
4. 44, 66, 88 6 5 4 22

14. Lesson Quiz: Part II
Find the greatest common factor of the set of numbers.
5. Mrs. Lovejoy makes flower arrangements. She has 36 red carnations, 60 white carnations, and 72 pink carnations. Each arrangement must have the same number of each color. What is the greatest number of arrangements she can make if every carnation is used?
12 arrangements

15. HOMEWORK
p : 1-18, 37-38