﻿ Prime Factorization Worksheets - Page 13 | Problems & Solutions

# Prime Factorization Worksheets - Page 13

Prime Factorization Worksheets
• Page 13
121.
Is 60 a prime or a composite number?
 a. Prime b. Composite c. Both prime and composite d. Neither prime nor composite

#### Solution:

The factors of 60 = 2 × 2 × 3 × 5.

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

So, 60 is a composite number.
[It has more than 2 factors.]

122.
Is 13 a prime or a composite number?
 a. Prime b. Composite c. Both prime and composite d. Neither prime nor composite

#### Solution:

The number 13 has no factors except one and itself.

A number which has no factors other than 1 and itself is called a prime number.

So, 13 is a prime number.

123.
What would be the prime factorization of the number 210?
 a. 2 x 7 x 15 b. 6 x 35 c. 2 x 3 x 5 x 7 d. None of the above

#### Solution:

So, the prime factorization of 210 = 2 x 3 x 5 x 7.

124.
What would be the prime factorization of the number 105?
 a. 3 x 5 x 7 b. 15 x 7 c. 3 x 35 d. none of the above

#### Solution:

So, the prime factorization of 105 is 3 x 5 x 7.

125.
What is the prime factorization of the number 1001?
 a. 13 × 77 b. 11 × 91 c. 11 × 91 d. 7 × 11 × 13

#### Solution:

So, the prime factorization of 1001 is 7 × 11 × 13.

126.
Express the prime factorization of the number 72 using exponents.
 a. 23 × 31 b. 23 × 32 c. 22 × 33 d. none of the above

#### Solution:

The prime factorization of 72 = 2 × 2 × 2 × 3 × 3.

2 × 2 × 2 × 3 × 3 = 23 × 32
[Convert product form to exponential form.]

The prime factorization of 72 in exponential form is 23 × 32.

127.
Express the prime factorization of the number 90 using exponents.
 a. 6 × 3 × 5 b. 2 × 32 × 5 c. 2 × 31 × 15 d. 6 × 15

#### Solution:

The prime factorization of 90 = 2 × 3 × 3 × 5.

2 × 3 × 3 × 5 = 2 × 32 × 5
[Convert product form to exponential form.]

The prime factorization of 90 in exponential form is 2 × 32 × 5.

128.
A prime factor is a positive integer with __________ factors.
 a. Three b. Two c. One d. None of the above

#### Solution:

A prime factor is a positive integer with two factors, one and itself.

So, the appropriate term in the blank is two.

129.
A prime factor is a positive integer that consists of factors, one and __________.
 a. many more b. one c. itself d. None of the above

#### Solution:

A prime factor is a positive integer that consists of two factors, one and itself.

So, the appropriate term in the blank is itself.

130.
Express the prime factorization of the number 375 using exponents.
 a. 32 × 5 b. 15 × 75 c. 3 × 52 d. 3 × 53

#### Solution:

The prime factorization of 375 = 3 × 5 × 5 × 5.

3 × 5 × 5 × 5 = 3 × 53
[Convert product form to exponential form.]

The prime factorization of 375 in exponential form is 3 × 53.