﻿ Prime Factorization Worksheets - Page 5 | Problems & Solutions # Prime Factorization Worksheets - Page 5

Prime Factorization Worksheets
• Page 5
41.
List all the prime numbers greater than 20 and less than 30. a. 23, 31, 29 b. 23 and 27 c. 23 and 29 d. 17 and 19

#### 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.

42.
Identify a number that is a multiple of 15. a. 384 b. 225 c. 275 d. 366

#### Solution:

When a number divided by 15 leaves a remainder zero, the number is a multiple of 15.

The numbers 384, 366, and 275 do not leave remainder zero when divided by 15.

The number 225 leaves a remainder zero when divided by 15.

Therefore, 225 is a multiple of 15.

43.
Which of the following is a factor of 121? a. 14 b. 12 c. 11 d. 13

#### Solution:

121 = 1 × 11 × 11

So, 11 is one of the factors of 121.

44.
Which of the following is a multiple of 25? a. 625 b. 112 c. 135 d. 220

#### Solution:

When a number divided by 25 leaves a remainder zero, the number is a multiple of 25.

The numbers 112, 135, and 220 do not leave remainder zero, when divided by 25.

The number 625 leaves a remainder zero, when divided by 25.

So, 625 is a multiple of 25.

45.
Identify the prime number. a. 57 b. 9 c. 13 d. 33

#### Solution:

A prime number has exactly two factors, 1 and itself.

Factors of 9 : 1, 3 and 9
Factors of 33 : 1, 3, 11, and 33
Factors of 57 : 1, 3, 19, and 57
Factors of 13 : 1 and 13

The numbers 9, 33, and 57 have more than 2 factors.

So, the number 13 is a prime number.

46.
Identify a prime number. a. 107 b. 51 c. 121 d. 93

#### Solution:

A prime number has exactly two factors, 1 and itself.

Factors of 51 : 1, 3, 17, and 51
Factors of 121 : 1, 11, and 121
Factors of 93 : 1, 3, 31, and 93
Factors of 107 : 1 and 107

The numbers 51, 121, and 93 have more than 2 factors.

So, the number 107 is a prime number.

47.
Identify a composite number. a. 113 b. 59 c. 35 d. 71

#### Solution:

A composite number has more than two factors.

Factors of 59 : 1, and 59
Factors of 71 : 1 and 71
Factors of 113 : 1 and 113
Factors of 35 : 1, 5, 7, and 35

The number 35 has more than two factors.

So, the number 35 is a composite number.

48.
Identify a prime number. a. 121 b. 109 c. 93 d. 39

#### Solution:

A prime number has exactly two factors, 1 and itself.

Factors of 39: 1, 3, 13, and 39.
Factors of 121 : 1, 11, and 121.
Factors of 93 : 1, 3, 31, and 93.
Factors of 109: 1 and 109.

The numbers 39, 121, and 93 have more than 2 factors.

So, the number 109 is a prime number.

49.
Identify a composite number. a. 119 b. 31 c. 71 d. 51

#### Solution:

A composite number has more than two factors.

Factors of 31: 1 and 31
Factors of 71: 1 and 71
Factors of 119: 1 and 119
Factors of 51: 1, 3, 17, and 51

The number 51 has more than two factors.

So, the number 51 is a composite number.

50.
Find all the common factors of 16, 28, and 32. a. 1, 2, 4, 5, and 10 b. 1, 2, and 4 c. 32, 56 and 64 d. 1, 2, 3 and 4

#### Solution:

16 = 1 × 16, 2 × 8, 4 × 4
[Write the pairs of numbers with a product of 16.]

The factors of 16 are 1, 2, 4, 8 and 16.

28 = 1 × 28, 2 × 14, 4 × 7
[Write the pairs of numbers with a product of 28.]

The factors of 28 are 1, 2, 4, 7, 14 and 28.

32 = 1 × 32, 2 × 16, 4 × 8
[Write the pairs of numbers with a product of 32.]

The factors of 32 are 1, 2, 4, 8, 16 and 32.

The common factors of 16, 28 and 32 are 1, 2 and 4.