﻿ Prime Factorization Worksheets - Page 12 | Problems & Solutions

# Prime Factorization Worksheets - Page 12

Prime Factorization Worksheets
• Page 12
111.
Using divisibility test, state whether 75 is a prime or a composite number.
 a. Composite b. Prime

#### Solution:

75 is divisible by 5, since it ends with 5.
[Use the divisibility test.]

So, 75 has more than two factors.

A whole number greater than 1 with more than two factors is called a composite number.

75 is a composite number.

112.
Using divisibility test, find whether 82 is a prime or a composite number.
 a. Prime b. Composite

#### Solution:

The one's digit of 82 is even

Since the one's digit of the number 82 is even, 82 is divisible by 2. It has more than two factors.
[Use the divisibility test.]

A whole number greater than 1 with more than two factors is called a composite number.

82 is a composite number.

113.
Using divisibility test, find whether 54 is a prime or a composite number.
 a. Prime b. Composite

#### Solution:

Since the sum of the digits of the number 54 is divisible by 9, 54 is divisible by 9.
[Use the divisibility test.]

It has more than two factors.

A whole number greater than 1 with more than two factors is called a composite number.

54 is a composite number.

114.
Which of the numbers 18, 13, 11 and 19 is composite?
 a. 11 b. 13 c. 18 d. 19

#### Solution:

A whole number greater than 1 with more than two factors is called a composite number.

The only divisors of 13, 11 and 19 are 1 and the numbers themselves.

Since the sum of the digits of the number 18 is divisible by 3, 18 is divisible by 3. It has more than two factors.
[Use the divisibility test.]

Among the numbers, the number 18 is a composite number.

115.
Write the prime factorization of 256 in exponential form using a factor tree.
 a. 25 b. 28 c. 27 d. 26

#### Solution:

Write the number 256 as a product of two factors and factorize all the composite factors.

256 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2
The prime factorization of 256 is:

256 = 28
[Write in the exponential form.]

The prime factorization of 256 is 28.

116.
Find the prime factorization of 325 using a factor tree.
 a. 52 × 131 b. 52 × 31 c. 52 × 132 d. 53 × 131

#### Solution:

Write the number 325 as a product of two factors and factorize the remaining composite factors.

The prime factors of 325 are: 325 = 5 × 5 × 13

325 = 52 × 131
[Write in the exponential form.]

The prime factorization of 325 is 52 × 131.

117.
Find the prime factorization of 160 in exponential form using a factor tree.
 a. 23 × 51 b. 25 × 52 c. 25 × 51 d. 24 × 51

#### Solution:

Write the number 160 as a product of two factors and factorize the composite factors.

160 = 2 × 2 × 2 × 2 × 2 × 5
The prime factorization of 160 is:

160 = 25 × 51
[Write in the exponential form.]

The prime factorization of 160 is 25 × 51.

118.
Express 18 as difference of two prime numbers.
 a. (29 - 11) b. (31 - 13) c. (30 - 12) d. (28 - 10)

#### Solution:

A whole number greater than 1 with exactly two factors 1 and itself is called a prime number.

18 can be expressed as a difference of two prime numbers in two ways, which is:29 - 11 = 18, 23 - 5 = 18 .

Among the choices, 18 is expressed as (29 - 11), which is the difference of two prime numbers.

119.
Which number in the set of numbers (2, 5, 9, 3) is a common factor among the prime factors of 4, 10 and 18?
 a. 5 b. 2 c. 9 d. 3

#### Solution:

The prime factors of 4 are: 4 = 2 x 2.

The prime factors of 10 are: 10 = 5 x 2.

The prime factors of 18 are: 18 = 3 x 3 x 2.

In the set of numbers, the number 2 is a common factor among the prime factors of 4, 10 and 18.

120.
Find the product of all the prime factors of 16.
 a. 4 b. 16 c. 21 d. 8

#### Solution:

The product of all the prime factors of any number is the number itself.

The product of all the prime factors of the number 16 is 16.