All the solutions provided in **McGraw Hill Math Grade 5 Answer Key PDF Chapter 2 Lesson 1 Prime Factorization** will give you a clear idea of the concepts.

## McGraw-Hill My Math Grade 5 Answer Key Chapter 2 Lesson 1 Prime Factorization

**Talk Math**

What are the first ten prime numbers?

**Guided Practice**

Question 1.

Find the prime factorization of 16.

The prime factorization of 16 is

____ × ____ × ____ × ____

Answer:

2 × 2 × 2 × 2

Explanation:

**Independent Practice**

**Find the prime factorization of each number.**

Question 2.

63 = ___

Answer:

3 × 3 × 7 = 3^{2} × 7

Explanation:

Question 3.

18 = ____

Answer:

2 × 3 × 3

Explanation:

Question 4.

40 = ___

Answer:

2 × 2 × 2 × 5

Explanation:

Question 5.

75 = ____

Answer:

3 × 5 × 5

Explanation:

Question 6.

27 = ___

Answer:

3 × 3 × 3

Explanation:

Question 7.

32 = ____

Answer:

2 × 2 × 2 × 2

Explanation:

Question 8.

49 = ____

Answer:

7 × 7

Explanation:

Question 9.

44 = ____

Answer:

11 × 4

11 × 2 × 2

Explanation:

**Mathematical PRACTICE 2 Understand Symbols Find the missing number.**

Question 10.

104 = 2 × 2 × × 13

= ___

Answer:

x = 2

Explanation:

Let us solve the expression to find the missing number

104 = 2 × 2 × x × 13

104 = 4 × x × 13

104 = 52x

x = 104 ÷ 52

x = 2

Question 11.

55 = × 11

= ___

Answer:

x = 5

Explanation:

Let us solve the expression to find the missing number

55 = x × 11

x = 55 ÷ 11

x = 5

Question 12.

77 = 7 ×

= ___

Answer:

x = 11

Explanation:

Let us solve the expression to find the missing number

77 = 7 × x

x = 77 ÷ 7

x = 11

**Problem Solving**

**Use the table for Exercises 13—16 that shows the average weights of popular dog breeds.**

Question 13.

Complete the table.

Answer:

Question 14.

Which weight(s) have a prime factorization of exactly three factors?

Answer:

The weights of cocker spaniel, Golden Retriever, and Siberian Husky.

Question 15.

Which weight(s) have a prime factorization with factors that are all the same number?

Answer:

Beagle

Explanation:

The weight of Beagle has factors that are all the same number.

Beagle 5 × 5

Question 16.

Which breed(s) have weights that are prime numbers?

Answer:

Labrador Retriever.

Explanation:

Labrador Retriever have weights that are prime numbers.

**Hot Problems**

Question 17.

**Mathematical PRACTICE Identify Structure** Find the prime factorization of 2,800.

Answer:

The prime factorization of 2,800 is 2^{4} × 5^{2} × 7^{1}

Explanation:

The prime factorization is 2^{4} × 5^{2} × 7^{1}

Question 18.

**? Building on the Essential Question** How do factor trees help you find the prime factorization of a number?

Answer:

First write the given number at the top of the factor tree and and draw two branches.

write the pair of branches with a pair of factor of the number above

Continue this step until each branch ends with a prime number.

Write the solution in a separate line.

### McGraw Hill My Math Grade 5 Chapter 2 Lesson 1 My Homework Answer Key

**Practice**

**Find the prime factorization of each number.**

Question 1.

50 = ____

Answer:

2 × 5 × 5

Explanation:

The prime factorization of the given number is 2 × 5 × 5.

Question 2.

81 = ___

Answer:

3 × 3 × 3 × 3

Explanation:

The prime factorization of the given number is 3 × 3 × 3 × 3

Question 3.

65 = ___

Answer:

5 × 13

Explanation:

The prime factorization of the given number is 5 × 13.

Question 4.

28 = ___

Answer:

2 × 2 × 7

Explanation:

The prime factorization of the given number is 2 × 2 × 7.

**Problem Solving**

Question 5.

Britney scored an 85 on her last math test. Write the prime factorization of 85.

Answer:

5 × 17

Explanation:

The prime factorization of 85 is 5 × 17.

Question 6.

Priscilla has 56 stickers in her collection. Write the prime factorization of 56.

Answer:

2 × 2 × 2 × 7

Explanation:

Given 56

we need to find the prime factorization.

Factor of 56

56 = 1 × 56, 2 × 28, 4× 14, 7 × 8

56 = 2 × 2 × 2 × 7

Question 7.

**Mathematical PRACTICE** 3 Find the Error Lainey wrote the prime factorization of 60 as 2 × 5 × 6. Is she correct? If not, what is the prime factorization of 60? Explain.

Answer:

She is not correct because 6 is not a prime number.

2 × 2 × 5 × 3

Explanation:

She is not correct because 6 is not a prime. It is a composite number. The answer for the prime factorization is 2 × 2 × 5 × 3.

**Vocabulary Check**

**Fill in each blank with the correct term or number to complete the sentence.**

Question 8.

___ numbers can be written as a product of factors. This is called the prime factorization of a number.

Answer:

Composite number.

Explanation:

Composite numbers can be written as a product of factors. This is called the prime factorization of a number.

**Test Practice**

Question 9.

Josiah had a pot belly pig as a pet that weighed 46 pounds. What is the prime factorization of 46?

A. 2 × 23

B. 2 × 2 × 11

C. 2 × 2 × 13

D. 3 × 23

Answer:

46 = 2 × 23

Explanation:

Josiah had a pot belly pig as a pet that weighed 46 pounds

Factors of 46 are 1, 2, 23 and 46

Prime factors = 2 and 23

The prime factorization of 46 is 46 = 2 × 23