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Warm Up

Problem of the Day

Lesson Presentation

Lesson Quizzes

Warm Up Write the prime factorization of each

number. 1. 14 3. 63 2. 18 4. 54

2 ? 7

32 ? 7

2 ? 33

2 ? 32

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

Sunshine State Standards

Prep for MA.6.A.5.1 Use equivalent forms of

fractions, decimalsto solve problems. Also

Review of MA.5.A.6.1

Vocabulary

greatest common factor (GCF)

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.

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,

14,

7,

28

4,

7,

1,

3,

2,

42

6,

21,

14,

Circle the GCF.

The GCF of 28 and 42 is 14.

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.

5

2

3

2

2

2

3

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.

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

5 2 3

Find the product of the numbers you divided by.

3 3

9

The GCF of 45, 18, and 27 is 9.

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,

9,

6,

18

3,

6,

1,

3,

2,

36

4,

12,

9,

Circle the GCF.

18,

The GCF of 18 and 36 is 18.

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

2

5

3

2

5

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.

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

5 2 3

Find the product of the numbers you divided by.

2 2 2

8

The GCF of 40, 16, and 24 is 8.

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?

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.

You can make an organized list of the possible

bouquets.

16 red, 24 yellow Every flower is in a bouquet

The greatest number of bouquets Jenna can make is

8.

Look Back

To form the largest number of bouquets, find the

GCF of 16 and 24. factors of 16 factors of 24

1,

8,

4,

2,

16

1,

3,

24

8,

2,

4,

6,

12,

The GCF of 16 and 24 is 8.

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?

Check It Out Example 2 Continued

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.

You can make an organized list of the possible

fruit baskets.

18 oranges, 27 pears Every fruit is in a basket

The greatest number of baskets Peter can make is

9.

Look Back

To form the largest number of baskets, find the

GCF of 18 and 27. factors of 18 factors of 27

1,

18

6,

9,

3,

2,

1,

9,

3,

27

The GCF of 18 and 27 is 9.

Lesson Quizzes

Standard Lesson Quiz

Lesson Quiz for Student Response Systems

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

Lesson Quiz Part II

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

Lesson Quiz for Student Response Systems

1. Identify the greatest common factor of 28 and

36. A. 2 B. 4 C. 6 D. 7

Lesson Quiz for Student Response Systems

2. Identify the greatest common factor of 49 and

77. A. 3 B. 5 C. 7 D. 11

Lesson Quiz for Student Response Systems

3. Identify the greatest common factor of 16, 24,

and 40. A. 2 B. 4 C. 5 D. 8

Lesson Quiz for Student Response Systems

4. Identify the greatest common factor of 42, 63,

and 84. A. 3 B. 7 C. 19 D. 21

Lesson Quiz for Student Response Systems

5. Harry collected 42 first-aid kits, 56

blankets, and 70 food packets for a flood-relief

camp. He wants to pack the collected items in

boxes in such a way that each box has the same

number of items of each kind. What is the

greatest number of boxes that Harry needs? A. 7

boxes B. 14 boxes C. 21 boxes D. 24 boxes