﻿ Prime Factorization Worksheets - Page 4 | Problems & Solutions # Prime Factorization Worksheets - Page 4

Prime Factorization Worksheets
• Page 4
31.
Which of the following numbers has only two factors? a. 17 b. 39 c. 21 d. 27

#### Solution:

Prime number is a number which has only two factors, 1 and itself.

Factors of 17 are 1 and 17.

Factors of 21 are 1, 3, 7, and 21.

Factors of 27 are 1, 3, 9, and 27.

Factors of 39 are 1, 3, 13, and 39.

Among the choices, the number that has only two factors is 17.

32.
Which of the following numbers has more than two factors? a. 31 b. 11 c. 29 d. 21

#### Solution:

A composite number is a number which has more than two factors.

Factors of 11 are 1 and 11.

Factors of 31 are 1 and 31.

Factors of 29 are 1 and 29.

Factors of 21 are 1, 3, 7, and 21.

Among the choices, the number that has more than two factors is 21.

33.
Identify the number that has only two factors. a. 10 b. 22 c. 2 d. 8

#### Solution:

Prime number is a number which has only two factors, 1 and itself.

Factors of 8 are 1, 2, 4, and 8.

Factors of 10 are 1, 2, 5, and 10.

Factors of 22 are 1, 2, 11, and 22.

Factors of 2 are 1 and 2.

Among the choices, the number that has only two factors is 2.

34.
Identify the number that has more than two factors. a. 51 b. 31 c. 37 d. 41

#### Solution:

A composite number is a number which has more than two factors.

Factors of 31 are 1 and 31.

Factors of 41 are 1 and 41.

Factors of 37 are 1 and 37.

Factors of 51 are 1, 3, 17, and 51.

Among the choices, the number that has more than two factors is 51.

35.
Choose the number that has more than two factors. a. 71 b. 57 c. 83 d. 43

#### Solution:

A composite number is a number which has more than two factors.

Factors of 43 are 1 and 43.

Factors of 83 are 1 and 83.

Factors of 71 are 1 and 71.

Factors of 57 are 1, 3, 19, and 57.

Among the choices, the number that has more than two factors is 57.

36.
Find the prime factorization of 28. a. 7 × 3 b. 23 × 7 c. 2 × 7 d. 22 × 7

#### Solution:

Use rules to find any two factors of the number and split these factors until all the factors are prime. The factor tree for 28 is shown below.
[28 = 4 × 7, 4 = 2 × 2]

The circled numbers in the factor tree are the prime factors of 28.

28 = 2 × 2 × 7

28 = 22 × 7
[Write in the form of exponents.]

The prime factorization of 28 is 22 × 7.

37.
List all the prime numbers greater than 20 and less than 30. a. 17 and 19 b. 23 and 29 c. 23 and 27 d. 23, 31, 29

#### Solution:

A number that has only two factors, one and itself is called a prime number.

List of prime numbers greater than 20 and less than 30 are 23 and 29.

38.
Find the prime factorization of 74. a. 2 × 37 b. 23 × 37 c. 22 × 37 d. 24 × 37

#### Solution:

Use rules to find any two factors of the number and split these factors until all the factors are prime. The factor tree for 74 is shown below.

The circled numbers in the factor tree are the prime factors of 74.

74 = 2 × 37

The prime factorization of 74 is 2 × 37.

39.
Find the prime factorization of 88. a. 11 × 22 b. 112 × 23 c. 112 × 22 d. 11 × 23

#### Solution:

Use rules to find any two factors and split these factors until all the factors are prime. The factor tree for the number 88 is shown below.
[88 = 22 × 4, 22 = 11 × 2, 4 = 2 × 2]

The circled numbers in the factor tree are the prime factors of 88.

88 = 11 × 2 × 2 × 2

88 = 11 × 23
[Write in the form of exponents.]

The prime factorization of 88 is 11 × 23.

40.
Find the prime factorization of 105. a. 5 × 72 × 3 b. 52 × 7 c. 5 × 7 × 3 d. 52 × 7 × 3

#### Solution:

Use rules to find any two factors and split these factors until all the factors are prime. The factor tree for 105 is shown below.
[105 = 5 × 21, 21 = 7 × 3]

The circled numbers in the factor tree are the prime factors of 105.

105 = 5 × 7 × 3

The prime factorization of 105 is 5 × 7 × 3.