We included **HMH Into Math Grade 4 Answer Key**** PDF** **Module 10 Lesson 4 Identify Prime and Composite Numbers** to make students experts in learning maths.

## HMH Into Math Grade 4 Module 10 Lesson 4 Answer Key Identify Prime and Composite Numbers

I Can determine whether a number is prime or composite.

**Step It Out
**1. A landscaper is buying palm trees. She wants to have several ways to plant the trees in equal rows. Should she buy 10 trees or 11 trees?

A. Show all the possible area models for 10 and 11. Label each area model with the factors it shows.

B. Identify the number that has more factors.

10 has ___ factors. 11 has ___ factors.

The number ___ has more factors.

C. The landscaper should buy _____ trees.

Answer:

The landscaper should buy 10 trees.

Explanation:

Number of trees = 10 or 11.

Factors of 10:

1 × 10 = 10.

2 × 5 = 10.

Factors of 11:

1 × 11 = 11.

She wants to have several ways to plant the trees in equal rows.

=> 2 rows × 5 plants = 10 plants.

**Connect to Vocabulary**

A prime number is a whole number greater than 1 that has exactly two factors, 1 and itself. A composite number is a whole number that has more than two factors.

**Step It Out
**2. Are the numbers 42 and 43 prime or composite?

A. Determine if each number is divisible by any number other than 1 and itself.

- 42 is even. So, ___ is divisible by 2.
- 43 is odd. So, ___ is not divisible by 2 or any multiple of 2.
- The sum of the digits in 43 is not divisible by 3. So, 43 is not divisible by ___ or any multiple of ___.

- 43 does not end in the digit 0 or 5. So, 43 is not divisible by ___ or any multiple of ___.
- 43 is not divisible by 7, 11, 13, 17, or 19.

B. Identify each number as prime or composite.

- 42 is divisible by a number other than 1 and itself.

So, 42 is a ___ number. - 43 is only divisible by 1 and itself. So, 43 is a ___ number.

Answer:

42 is composite number and 43 is a prime number because 42 has many factors and divisible by 2 yet 43 has one and itself as factors and cannot be divisible by 2.Explanation:

Numbers 42 and 43 prime or composite

Factors of 42:

1 × 42 = 42.

2 × 21 = 42.

3 × 14 = 42.

6 × 7 = 42.

Factors of 43:

1 × 43 = 43.

**Turn and Talk** Why do you need to know that 43 is not divisible by 7, 11, 13, 17, or 19 to know for sure whether 43 is prime or composite?

Answer:

It is important to know that 43 is not divisible by 7, 11, 13, 17, or 19 to know for sure whether 43 is prime or composite because its if is divisible by prime number 7, 11, 13, 17, or 19 then its divisible by all that numbers.

Explanation:

Factors of 43:

1 × 43 = 43.

**Check Understanding Math Board
**

**Tell whether the number is prime or composite.**

Question 1.

72 _____

Answer:

72 is composite number because it has many factors and divisible by 2.

Explanation:

72

Factors of 72:

1 × 72 = 72.

2 × 36 = 72.

3 × 24 = 72.

4 × 18 = 72.

6 × 12 = 72.

8 × 9 = 72.

Question 2.

53 ______

Answer:

53 is a prime number as it has 1 itself as factors and not divisible by 2.

Explanation:

Factors of 53:

1 × 53.

Question 3.

87 _____

Answer:

87 is a composite number as it has many others factors.

Explanation:

factors of 87:

1 × 87 = 87.

3 × 29 = 87.

**On Your Own
**Question 4.

Violet wants to plant flower seeds in an array. She wants to have several options for the array.

- Which pack of seeds should she buy?

__________________________ - What are the possible arrays?

__________________________

__________________________

Answer:

Pack of seeds should she buy is 48 because it can be arranged in 2,3,4,6,8,12,16,24 arrays yet not 43.Explanation:

Pack of seeds:

Packet of 47 seeds:

Factors of 47:

1 × 47 = 47.

Factors of 48:

1 × 48 = 48.

2 × 24 = 48.

3 × 16 = 48.

4 × 12 = 48.

6 × 8 = 48.

Question 5.

**Use Structure** Is the product of two prime numbers a prime number or a composite number? Explain.

__________________________

__________________________

Answer:

No, the product of two prime numbers is not prime.

Explanation:

Prime number × Prime number = ???

For example:

3 × 7 = 21.

7 × 7 = 49.

**Tell whether the number is prime or composite.
**Question 6.

61

__________________________

Answer:

61 is a prime number because it has 1 and itself as factors.

Explanation:

Factors of 61:

1 × 61 = 61.

Question 7.

14

__________________________

Answer:

14 is a composite number because it has more than 2 factors.

Explanation:

Factors of 14:

1 × 14 = 14.

2 × 7 = 14.

Question 8.

29

__________________________

Answer:

29 is a prime number because it has 1 and itself as factors.

Explanation:

Factors of 29:

1 × 29 = 29.

Question 9.

93

__________________________

Answer:

93 is a composite number because it has more than 2 factors.

Explanation:

Factors of 93:

1 × 93 = 93.

3 × 31 = 93.

Question 10.

2

__________________________

Answer:

2 is a prime number because it has 1 and itself as factors.

Explanation:

Factors of 2:

1 × 2 = 2.

Question 11.

97

__________________________

Answer:

97 is a prime number because it has 1 and itself as factors.

Explanation:

Factors of 97:

1 × 97 = 97.

Question 12.

19

__________________________

Answer:

19 is a prime number because it has 1 and itself as factors.

Explanation:

Factors of 19:

1 × 19 = 19.

Question 13.

50

__________________________

Answer:

50 is a composite number because it has more than 2 factors.

Explanation:

Factors of 50:

1 × 50 = 50.

2 × 25 = 50.

5 × 10 = 50.

Question 14.

83

__________________________

Answer:

83 is a prime number because it has 1 and itself as factors.

Explanation:

Factors of 83:

1 × 83 = 83.

Question 15.

**Construct Arguments** The number 1 is neither prime nor composite because it only has 1 factor. Some people think that 1 should be classified as a prime number. Do you agree? Explain your answer.

Answer:

Yes, I agree because it only has 1 factor and itself.

Explanation:

Number 1 is a prime number because it only has 1 factor and itself.

**On Your Own
Reason
**Question 16. A number has exactly three factors, and one of the factors is 7. What is the number? Explain how you know.

Answer:

The number is 49 which has exactly three factors, and one of the factors is 7.

Explanation:

A number has exactly three factors, and one of the factors is 7.

Multiples of 7:

1 × 7 = 7. => Factors of 7: 1,7.

2 × 7 = 14. => Factors of 14: 1,2,7,14.

3 × 7 = 21. => Factors of 21: 1,3,7,21.

4 × 7 = 28. => Factors of 2: 1,2,4,7,14,28.

5 × 7 = 35. => Factors of 35: 1,5,7,35.6

6 × 7 = 42. => Factors of 42: 1,2,3,6,7,14,21.

7 × 7 = 49. => Factors of 49: 1,7,49.

Question 17.

**Open Ended** Find two numbers between 70 and 79 that are composite. Then find two numbers between 70 and 79 that are prime.

Answer:

Two numbers between 70 and 79 that are composite are 72,74,75,76,78.

Two numbers between 70 and 79 that are prime are 71 and 73.

Explanation:

Numbers between 70 and 79: 71,72,73,74,75,76,77,78.

Factors of 71:

1 × 71 = 71.

Factors of 72:

1 × 72 = 72.

2 × 36 = 72.

3 × 24 = 72.

4 × 18 = 72.

6 × 12 = 72.

8 × 9 = 72.

Factors of 73:

1 × 73 = 73.

Factors of 74:

1 × 74 = 74.

2 × 37 = 74.

Factors of 75:

1 × 75 = 75.

3 × 25 = 75.

5 × 15 = 75.

Factors of 76:

1 × 76 = 76.

2 × 38 = 76.

4 × 19 = 76.

Factors of 77:

1 × 77 = 77.

7 × 11 = 77.

Factors of 78:

1 × 78 = 78.

2 × 39 = 78.

3 × 26 = 78.

6 × 13 = 78.

**Construct Arguments** Write true or false for the statement. Explain or give an example to support your answer.

Question 18.

All even numbers are composite numbers.

Answer:

False, all even numbers are not composite because the number 2 is even but is not a composite number.

Explanation:

All even numbers are not composite. This is because the number 2 is even but is not a composite number. The number 2 only has two factors, 1 and 2. Because of this, it doesn’t meet the definition of a composite number.

Question 19.

All prime numbers have exactly one factor pair.

Answer:

True, all prime numbers have exactly one factor pair because any prime number will have only a single factor pair.

Explanation:

Any prime number will have only a single factor pair.

Example: for the prime number 17: 17 × 1 = 17, therefore it has only one factor pair.

Question 20.

All multiples of 4 are composite numbers.

Answer:

True, all multiples of 4 are composite numbers because they have more than two factors.

Explanation:

All multiples of 4 are composite numbers.

For example:

4 × 4 = 16.

Factors of 16 = 1 × 16 = 16.

2 × 8 = 16.

4 × 4 = 16.

Question 21.

**Use Tools** Jada was born in October. Her birth date is a prime number. Circle all the dates on this calendar that could be Jada’s birth date. The calendar shows that Jada’s birth date falls on a Monday. What is her birth date?

Answer:

Date of birth of Jada can be 1 or 29.

Explanation:

Jada was born in October.

Her birth date is a prime number.

Number of days of Mondays in October:

1,8,15,22,29.

Factors of

1: 1 × 1 = 1.

8: 1 × 8 = 8.

2 × 4 = 8.

15: 1 × 15 = 15.

3 × 5 = 15.

22: 1 × 22 = 22.

2 × 11 = 22.

29: 1 × 29 = 29.