1. Greatest Common Factor
4-3
Greatest Common Factor
Course 1
Warm Up
Problem of the Day
Lesson Presentation

2. Greatest Common Factor
Course 1
4-3
Greatest Common Factor
Warm Up
Write the prime factorization of each number.
2  7
32  7
2  32
2  33

3. Greatest Common Factor
Course 1
4-3
Greatest Common Factor
Problem of the Day
In a parade, there are 15 riders on bicycles and tricycles. In all, there are 34 cycle wheels. How many bicycles and how many tricycles are in the parade?
11 bicycles and 4 tricycles

4. Greatest Common Factor
Course 1
4-3
Greatest Common Factor
Learn to find the greatest common factor (GCF) of a set of numbers.

5. Insert Lesson Title Here
Course 1
4-3
Greatest Common Factor
Insert Lesson Title Here
Vocabulary
greatest common factor (GCF)

6. Greatest Common Factor
Course 1
4-3
Greatest Common Factor
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.

7. Additional Example 1A: Finding the GCF
Course 1
4-3
Greatest Common Factor
Additional Example 1A: Finding the GCF
Find the GCF of the set of numbers.
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.

8. Additional Example 1B: Finding the GCF
Course 1
4-3
Greatest Common Factor
Additional Example 1B: Finding the GCF
Find the GCF of the set of numbers.
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 product of the common prime factors.
2 • 3 = 6
The GCF of 18, 30, and 24 is 6.

9. Additional Example 1C: Finding the GCF
Course 1
4-3
Greatest Common Factor
Additional Example 1C: Finding the GCF
Find the GCF of the set of numbers.
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.

10. Greatest Common Factor
Course 1
4-3
Greatest Common Factor
Check It Out: Example 1A
Find the GCF of the set of numbers.
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.

11. Greatest Common Factor
Course 1
4-3
Greatest Common Factor
Check It Out: Example 1B
Find the GCF of the set of numbers.
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 product of the common prime factors.
2 • 5 = 10
The GCF of 10, 20, and 30 is 10.

12. Greatest Common Factor
Course 1
4-3
Greatest Common Factor
Check It Out: Example 1C
Find the GCF of the set of numbers.
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.

13. Additional Example 2: Problem Solving Application
Course 1
4-3
Greatest Common Factor
Additional 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?

14. Understand the Problem
Course 1
4-3
Greatest Common Factor 1
Understand the Problem
The answer will be the greatest number of bouquets 16 red flowers and 24 yellow flowers can form so that each bouquet has the same number of red flowers, and each bouquet has the same number of yellow flowers. 2
Make a Plan
You can make an organized list of the possible bouquets.

15. Greatest Common Factor
Course 1
4-3
Greatest Common Factor
Solve 3
Red
Yellow
Bouquets 2 3 RR
YYY RR
YYY RR
YYY RR
YYY RR
YYY RR
YYY RR
YYY RR
YYY
16 red, 24 yellow:
Every flower is in a bouquet
The greatest number of bouquets Jenna can make is 8. 4
Look Back
To form the largest number of bouquets, find the GCF of 16 and 24. factors of 16:
factors of 24: 1, 2, 4, 8, 16 1, 2, 3, 4, 6, 8,
12, 24
The GCF of 16 and 24 is 8.

16. Greatest Common Factor
Course 1
4-3
Greatest Common Factor
Check It Out: 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?

17. Understand the Problem
Course 1
4-3
Greatest Common Factor
Check It Out: Example 2 Continued 1
Understand the Problem
The answer will be the greatest number of fruit baskets 18 oranges and 27 pears can form so that each basket has the same number of oranges, and each basket has the same number of pears. 2
Make a Plan
You can make an organized list of the possible fruit baskets.

18. Greatest Common Factor
Course 1
4-3
Greatest Common Factor
Solve 3
Oranges
Pears
Bouquets 2 3 OO
PPP OO
PPP OO
PPP OO
PPP OO
PPP OO
PPP OO
PPP OO
PPP OO
PPP
18 oranges, 27 pears:
Every fruit is in a basket
The greatest number of baskets Peter can make is 9. 4
Look Back
To form the largest number of bouquets, find the GCF of 18 and 27. factors of 18:
factors of 27: 1, 2, 3, 6, 9, 18 1, 3, 9, 27
The GCF of 18 and 27 is 9.

19. Greatest Common Factor Insert Lesson Title Here
Course 1
4-3
Greatest Common Factor
Insert Lesson Title Here
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

20. Greatest Common Factor Insert Lesson Title Here
Course 1
4-3
Greatest Common Factor
Insert Lesson Title Here
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