All the solutions provided in **McGraw Hill Math Grade 5 Answer Key PDF Chapter 8 Lesson 2 Greatest Common Factor** will give you a clear idea of the concepts.

## McGraw-Hill My Math Grade 5 Answer Key Chapter 8 Lesson 2 Greatest Common Factor

**Math in My World**

Example 1

Sevierville Middle School arranges their sports trophies in rows in a display case. There is an equal number of trophies in each row. Each row has only one kind of trophy. What is the greatest possible number of trophies in each row?

Write the prime factorization to find common factors.

The common prime factors are 2, 2, and 2.

Multiply to find the GCF.

____ × ___ × ___ or ____

Answer:

2 × 2 × 2 = 8

So, the greatest number of trophies that could be placed in each row is 8.

Example 2

Find the GCF of 60 and 54.

Make an organized list of the factors for each number. Then circle the common factors.

60:1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

54: 1, 2, 3, 6, 9, 18, 27, 54

The common factors are 1 , 2, 3, 6.

So, the greatest common factor, or GCF, of 60 and 54 is 6.

**Guided Practice**

**Find the GCF of each set of numbers.**

Question 1.

8, 32

8: _______

32: _______

The common factors are ___, ___, ___, and ____

So, the GCF of 8 and 32 is ____.

Answer:

The factors of 8 = 1, 2, 4, 8

The factors of 32 = 1, 2, 4, 8, 16, 32

Explanation:

The common factors are 1 , 2 , 4 and 8

So, the GCF of 8 and 32 is 8

**Talk Math**

Explain which method you prefer to find the GCF of two numbers.

Answer:

Listing out common factors

Explanation:

In this method, factors of both the numbers can be listed, then it becomes easy to check for the common factors.

By marking the common factors, we can choose the greatest one amongst all of them.

Question 2.

3, 12, 18

3: ____

12: ____

18: ____

The common factors are ___ and ____

So, the GCF of 3, 12, and 18 is _____.

Answer:

Factors of 3 = 1, 3

The factors of 12 = 1, 2, 3, 4, 6, 12

The factors of 18 are 1, 2, 3, 6, 9, 18

Explanation:

The common factors are 1 and 3

So, the GCF of 3, 12, and 18 is 3

**Independent Practice**

**Find the GCF of each set of numbers.**

Question 3.

24, 60 ____

Answer:

12

Explanation:

The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24.

The factors of 60 = 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60.

The common factors are 1, 2 , 3 , 4 ,6, 12

So, the GCF of 24 and 60 is 12

Question 4.

12, 18 ____

Answer:

6

Explanation:

The factors of 12 = 1, 2, 3, 4, 6, 12.

The factors of 18 = 1, 2, 3, 6, 9, 18

The common factors are 1, 2, 3 and 6.

So, the GCF of 12 and 18 is 6

Question 5.

18, 42 ____

Answer:

6

Explanation:

The factors of 18 = 1, 2, 3, 6, 9, 18

The factors of 42 = 1, 2, 3, 6, 7, 14, 21, 42

The common factors are 1, 2, 3 and 6.

So, the GCF of 18 and 42 is 6

Question 6.

30, 72 ____

Answer:

6

Explanation:

The factors of 30 = 1, 2, 3, 5, 6, 10, 15, 30

The factors of 72 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72

The common factors are 1, 2, 3 and 6.

So, the GCF of 30 and 72 is 6

Question 7.

4, 10, 14 ____

Answer:

2

Explanation:

The factors of 4 = 1, 2 and 4

The factors of 10 = 1, 2, 5 and 10

The factors of 14 = 1, 2, 7 and 14

The common factors are 1, 2

So, the GCF of 4, 10, 14 is 2

Question 8.

14, 35, 84 ____

Answer:

7

Explanation:

The factors of 14 = 1, 2, 7 and 14

The factors of 35 = 1, 5, 7 and 35

The factors of 84 = 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42 and 84

The common factors are 1, 2 , 7

So, the GCF of 14, 35, 84 is 7

Question 9.

9, 18, 42 ____

Answer:

3

Explanation:

The factors of 9 = 1, 3 and 9

The factors of 18 = 1, 2, 3, 6, 9, 18

The factors of 42 = 1, 2, 3, 6, 7, 14, 21, 42

The common factors are 1, 3

So, the GCF of 9, 18, 42 is 3

Question 10.

16, 52, 76 ____

Answer:

4

Explanation:

The factors of 16 = 1, 2, 4, 8 and 16

The factors of 52 = 1, 2, 4, 13, 26 and 52

The factors of 76 = 1, 2, 4, 19, 38, and 76.

The common factors are 1, 2 , 4

So, the GCF of 16, 52, 76 is 4

**Problem Solving**

Question 11.

**Mathematical PRACTICE 3 Justify Conclusions** Annika is placing photos in a scrapbook. Each page will have only one size of photo. She also wants to place the same amount of photos on each page. What is the greatest number of photos that could be on each page? Justify your response.

Answer:

4

Explanation:

The factors of 8 = 1, 2, 4, 8

The factors of 12 = 1, 2, 3, 4, 6, 12

The factors of 16 = 1, 2, 4, 8 and 16

The common factors are 1, 2 , 4

So, the greatest number of photos that could be on each page is the GCF of 8 , 12 , 16 is 4

Question 12.

Twelve pens and 16 pencils will be placed in bags with an equal number of each item. What is the most number of bags that can be made?

Answer:

4

Explanation:

The factors of 12 = 1, 2, 3, 4, 6, 12

The factors of 16 = 1, 2, 4, 8 and 16

The common factors are 1, 2 , 4

Four bags can be made as 12/4 is 3 and 16/4 is 4

Each bag could have 3 pens and 4 pencils

The most number of bags that can be made are 4 with an equal number of each item.

Question 13.

Oliver has 14 chocolate chip cookies and 21 iced cookies. Oliver gives each of his friends an equal number of each type of cookie. What is the greatest number of friends with whom he can share the cookies?

Answer:

7

Explanation:

The factors of 14 = 1, 2, 7 and 14.

The factors of 21 = 1, 3, 7 and 21.

The common factors are 1, 7

So. the GCF of 14 and 21 is 7

7 friends each get 2 chocolate and 3 iced.

**HOT Problems**

Question 14.

**Mathematical PRACTICE 3 Which One Doesn’t Belong?** Circle the number that you would take away so that 8 will be the GCF of the remaining three numbers.

Answer:

Explanation:

The factors of 8 = 1, 2, 4, 8

The factors of 16 = 1, 2, 4, 8 and 16

The factors of 24= 1, 2, 3, 4, 6, 8, 12 and 24

The common factors are 1, 2 , 4 , 8

So, the GCF of 8 , 12 , 24 is 8

20 is the number we have to take away.

Question 15.

**? Building on the Essential Question** How can you find the greatest common factor of two numbers?

Answer:

The greatest common factor is the greatest factor that divides both numbers. To find the greatest common factor, first list the prime factors of each number.

Explanation:

The factors of 12 = 1, 2, 3, 4, 6, 12.

The factors of 18 = 1, 2, 3, 6, 9, 18

The common factors are 1, 2 , 3, 6

So, the GCF of 12 and 18 is 6

### McGraw Hill My Math Grade 5 Chapter 4 Lesson 2 My Homework Answer Key

**Practice**

**Find the GCF of each set of numbers.**

Question 1.

21, 30 ____

Answer:

3

Explanation:

The factors of 21 =1, 3, 7 and 21.

The factors of 30 = 1, 2, 3, 5, 6, 10, 15 and 30.

The common factors are 1, 3

So, the GCF of 21, 30 is 3

Question 2.

12, 30, 72 ___

Answer:

6

Explanation:

The factors of 12 = 1, 2, 3, 4, 6, 12.

The factors of 30 = 1, 2, 3, 5, 6, 10, 15 and 30.

The factors of 72 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72

The common factors are 1, 2 , 3, 6

So, the GCF of 12, 30, 72 is 6

**Problem Solving**

Question 3.

A store sells boxes of juice in equal-size packs. Garth bought 18 boxes, Rico bought 36 boxes, and Mai bought 45 boxes. What is the greatest number of boxes in each pack? How many packs did each person buy if each box contained the greatest number of boxes possible?

Answer:

9

Explanation:

The factors of 18 = 1, 2, 3, 6, 9, 18

The factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36.

The factors of 45 = 1, 3, 5, 9, 15, 45.

The common factors are 1, 2 ,9

So, the GCF of 18 , 36, 45 is 9

The greatest number of boxes in each pack is 9

Garth bought 2 , Rico bought 4 , Mai bought 5

Question 4.

**Mathematical PRACTICE 3 Justify Conclusions** The GCF of any two even numbers is always even. Determine whether the statement is true or false. If true, explain why. If false, give a reason.

Answer:

Even

Explanation:

All even numbers have two as a factor.

That means that any set of even numbers will have at least a two as a common factor.

Since 2 will be a part of the greatest common factor, it will have to be even.

**Vocabulary Check**

Question 5.

Circle the correct term that makes the sentence true.

The (greatest, least) of the common factors of two or more numbers is the (greatest, least) common factor of the numbers.

Answer:

greatest , greatest

Explanation:

The (greatest) of the common factors of two or more numbers is the (greatest) common factor of the numbers.

**Test Practice**

Question 6.

Jeremiah will share his collection with his friends so that they each receive the same number of cards. What is the greatest number of cards they will each receive?

A. 4 cards

B. 8 cards

C. 12 cards

D. 16 cards

Answer:

B

Explanation:

The factors of 32 = 1, 2, 4, 8, 16, 32, 64

The factors of 24 = 1, 2, 3, 4, 6, 8, 12 and 24.

The common factors are 1, 2 , 4, 8

So. the GCF of 32 and 24 is 8

The greatest number of cards they will each receive is 8