Five-Minute Check (over Chapter 3)

Main Idea and Vocabulary

Example 1:Identify Common Factors

Example 2:Find the GCF by Listing Factors

Example 3:Find the GCF by Using Prime Factors

Example 4:Use the GCF to Solve a Problem

Example 5:Use the GCF to Solve a Problem

• Venn diagram

• common factor

• greatest common factor (GCF)

• Find the greatest common factor of two or more numbers.

• Venn Diagram example: page 197

Identify Common Factors

Identify the common factors of 20 and 36.

First, list the factors by pairs for each number.

Answer: The common factors are 1, 2, and 4.

Circle the common factors.

1. A

2. B

3. C

4. D

1. A

2. B

3. C

4. D0% 0% 0% 0%

Identify the common factors of 24 and 42.

A. 1, 2, and 3

B. 1, 6, and 12

C. 1, 2, 3, and 6

D. 1, 2, 3, 6, and 8

Find the GCF by Listing Factors

Find the GCF of 36 and 48.

First, make an organized list of the factors for each number.

36: 1 × 36, 2 × 18, 3 × 12, 4 × 9, 6 × 6 → 1, 2, 3, 4, 6, 9, 12, 18, 36

48: 1 × 48, 2 × 24, 3 × 16, 4 × 12, 6 × 8 → 1, 2, 3, 4, 6, 8,12, 16, 24,

48The common factors are 1, 2, 3, 4, 6, and 12, and the greatest of these is 12. So, the greatest common factor or GCF of 36 and 48 is 12.

Find the GCF by Listing Factors

Use a Venn diagram to show the factors. Notice that the factors 1, 2, 3, 4, 6, and 12 are the common factors of 36 and 48 and the GCF is 12.

Answer: The GCF is 12.

1. A

2. B

3. C

4. D0% 0%0%0%

Find the GCF of 45 and 75.

A. 3

B. 5

C. 9

D. 15

Find the GCF by Using Prime Factors

Find the GCF of 52 and 78.

Method 1 Write the prime factorization.

2 and 13are common

factors.

Find the GCF by Using Prime Factors

Method 2 Divide by prime numbers.

Using either method, the common prime factors are 2 and 13.

Answer: So, the GCF of 52 and 78 is 2 × 13 or 26.

Divide both 52 and 78 by 2.

Divide the quotients by 13.

1. A

2. B

3. C

4. D0% 0%0%0%

Find the GCF of 64 and 80.

A. 4

B. 8

C. 16

D. 32

SALES Anna sells bags of different kinds of cookies. She made $27 selling bags of peanut butter cookies, $18 from chocolate chip cookies, and $45 selling bags of oatmeal cookies. Each bag of cookies costs the same amount. What is the most that Anna could charge for each bag of cookies?

factors of 18: 1, 2, 3, 6, 9, 18

factors of 27: 1, 3, 9, 27

factors of 45: 1, 3, 5, 9, 15, 45

Answer: So, the most she could charge for each bag is $9.

Use the GCF to Solve a Problem

List all the factors of each number. Then find the greatest common factor.

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

1. A

2. B

3. C

4. D0% 0%0%0%

A. $6

B. $8

C. $10

D. $12

CANDY Sarah made boxes of different kinds of candy for a school fund-raiser. She made $24 selling boxes of hard candy, $40 from taffy, and $64 from chocolates. Each box of candy cost the same amount. What is the most that Sarah could charge for each box of candy?

Use the GCF to Solve a Problem

SALES Anna sells bags of different kinds of cookies. She made $27 selling bags of peanut butter cookies, $18 from chocolate chip cookies, and $45 selling bags of oatmeal cookies. How many bags could Anna have sold if each bag costs $9?

Anna has a total of $27 + $18 + $45 or $90. So, the number of bags sold is $90 ÷ $9 or 10.

Answer: 10 bags

Interactive Lab:Greatest Common Factor

1. A

2. B

3. C

4. D

0% 0%0%0%

A. 8 boxes

B. 11 boxes

C. 13 boxes

D. 16 boxes

CANDY Sarah made boxes of different kinds of candy for a school fund-raiser. She made $24 selling boxes of hard candy, $40 from taffy, and $64 from chocolates. How many boxes could Sarah have sold if each box costs $8?

End of the Lesson

Five-Minute Check (over Chapter 3)

Image Bank

Math Tools

Animation Menu

Greatest Common Factor

4-2 Equivalent Fractions

4-9 Ordered Pairs and Functions

1. A

2. B

3. C

4. D0% 0%0%0%

(over Chapter 3)

Find 43.489 + 71.156.

A. 114.745

B. 114.645

C. 114.635

D. 113.345

1. A

2. B

3. C

4. D0% 0%0%0%

(over Chapter 3)

Find 87.49 – 4.239.

A. 83.701

B. 83.260

C. 83.251

D. 83.161

1. A

2. B

3. C

4. D0% 0%0%0%

(over Chapter 3)

A. 6.70

B. 10.873

C. 11.9

D. 12.783

Find 2.62 × 4.15.

1. A

2. B

3. C

4. D0% 0%0%0%

(over Chapter 3)

A. 21.4

B. 21.7

C. 24.1

D. 42.1

Find 96.4 ÷ 4.

1. A

2. B

3. C

4. D0% 0%0%0%

(over Chapter 3)

A. 2.4

B. 3.2

C. 3.8

D. 4

Find 3.88 ÷ 0.97.

1. A

2. B

3. C

4. D

0% 0%0%0%

(over Chapter 3)

A. $16

B. $18

C. $20

D. $21

McKayla bought a picture frame that cost $6.95, a candle that cost $3.25, and a bottle of lotion that cost $5.85. Which of the following is the most reasonable total for the items purchased?