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4-2 Greatest Common Factor

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Lesson PresentationLesson Presentation

Problem of the DayProblem of the Day

Lesson QuizzesLesson Quizzes


Warm UpWrite the prime factorization of each number.

1. 14 3. 63

2. 18 4. 54

2 7 32 7

2 32 2 33


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


I can find the greatest common factor (GCF) of a set of numbers.


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,

1, 2, 3, 4, 6,

The greatest common factor (GCF) of 24 and 36 is 12.

Example 1 shows three different methods for finding the GCF.

1, 2, 3, 4, 6, 9,

12,

12, 18,

24

36

12


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:

1, 2, 14, 7, 28

7, 1,

4,

3, 2, 42 6, 21, 14,

List all the factors.

Circle the GCF.

The GCF of 28 and 42 is 14.


Additional Example 1B: Finding the GCF


18, 30, and 24

Method 2: Use the prime factorization.

18 =

30 =

24 =

2

5 •

3

2

2

3

2

3

23

Write the prime factorization of each number.

Find the common prime factors.

The GCF of 18, 30, and 24 is 6.

•

•

•

•

•

•

Find the prime factors common to all the numbers.

2 • 3 = 6


Additional Example 1C: Finding the GCF


45, 18, and 27

Method 3: Use a ladder diagram.

3

3

5 2 3

45 18 27 Begin with a factor that divides into each number. Keep dividing until the three have no common factors.

Find the product of the numbers you divided by.

3 • 3 =


9

15 6 9


Check It Out: Example 1A


18 and 36

Method 1: List the factors.

factors of 18:

factors of 36:

1, 2, 9, 6, 18

6, 1,

3,

3, 2, 36 4, 12, 9,

List all the factors.

Circle the GCF.


18,


Check It Out: Example 1B


10, 20, and 30

Method 2: Use the prime factorization.

10 =

20 =

30 =

2

2 •

3

2

5

2

5

5

Write the prime factorization of each number.

Find the common prime factors.


•

•

•

•

Find the prime factors common to all the numbers.

2 • 5 = 10


Check It Out: Example 1C


40, 16, and 24

Method 3: Use a ladder diagram.

2

2

40 16 24 Begin with a factor that divides into each number. Keep dividing until the three have no common factors.

Find the product of the numbers you divided by.

2 • 2 • 2 =


8

20 8 12

5 2 3 10 4 62


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?


22 Make a Plan

You can make an organized list of the possible bouquets.

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.

11 Understand the Problem


Solve33

The greatest number of bouquets Jenna can make is 8.

32

BouquetsYellowRedRR

YYY

16 red, 24 yellow:

Every flower is in a bouquet

RR

YYY

RR

YYY

RR

YYY

RR

YYY

RR

YYY

RR

YYY

RR

YYY

Look Back44To form the largest number of bouquets, find the GCF of 16 and 24. factors of 16:

factors of 24:

1,

4, 2,

16

8,

1,

3, 24

8, 2, 4, 6, 12,



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?


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.

11 Understand the Problem

22 Make a Plan

You can make an organized list of the possible fruit baskets.

Check It Out: Example 2 Continued


Solve33

The greatest number of baskets Peter can make is 9.

32

BouquetsPearsOranges

OO

PPP

18 oranges, 27 pears:

Every fruit is in a basket

OO

PPP

OO

PPP

OO

PPP

OO

PPP

OO

PPP

OO

PPP

OO

PPP

Look Back44

To form the largest number of baskets, find the GCF of 18 and 27. factors of 18:

factors of 27:

1,

3, 2,

18

6,

1,

9, 3, 27


OO

PPP

9,


Standard Lesson Quiz

Lesson Quizzes

Lesson Quiz for Student Response Systems


Lesson Quiz: Part I

1. 18 and 30

2. 20 and 35

3. 8, 28, 52

4. 44, 66, 88

5

6

4

22

Find the greatest common factor of each set of numbers.


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?

Find the greatest common factor of the set of numbers.

12 arrangements



1. Identify the greatest common factor of 28 and 36.

A. 2

B. 4

C. 6

D. 7



2. Identify the greatest common factor of 49 and 77.

A. 3

B. 5

C. 7

D. 11



3. Identify the greatest common factor of 16, 24, and 40.

A. 2

B. 4

C. 5

D. 8



4. Identify the greatest common factor of 42, 63, and 84.

A. 3

B. 7

C. 19

D. 21



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

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