﻿ Prime Factorization Worksheets - Page 9 | Problems & Solutions

# Prime Factorization Worksheets - Page 9

Prime Factorization Worksheets
• Page 9
81.
Write the prime factorization of 2 × 2 × 2 × 3 × 3 × 5 using exponents.
 a. 23 × 32 × 51 b. 23 × 33 × 52 c. 23 × 32 × 52 d. 23 × 32 × 53

#### Solution:

2 × 2 × 2 × 3 × 3 × 5
[Original expression.]

The prime factorization has three 2's, two 3's and one 5's.

= 23 × 32 × 51
[Write in exponential form.]

82.
Write the prime factorization of 2 × 2 × 2 × 2 × 7 × 3 × 3 using exponents.
 a. 24 × 71 × 33 b. 24 × 71 × 32 c. 24 × 72 × 32 d. 24 × 71 × 34

#### Solution:

2 × 2 × 2 × 2 × 7 × 3 × 3

There are four 2's, one 7 and two 3's in the prime factorization.

= 24 × 71 × 32
[Write in exponential form.]

83.
Write the prime factorization of 3 × 3 × 3 × 3 × 7 × 7 × 7 × 5 × 5 using exponents.
 a. 34 × 73 × 52 b. 34 × 73 × 53 c. 33 × 73 × 52 d. 34 × 74 × 52

#### Solution:

There are four 3's, three 7's and two 5's in the prime factorization.

3 × 3 × 3 × 3 × 7 × 7 × 7 × 5 × 5 = 34 × 73 × 52

84.
Write the prime factorization of 5 × 5 × 5 × 5 × 7 × 3 using exponents.
 a. 55 × 71 × 31 b. 54 × 71 × 32 c. 54 × 72 × 31 d. 54 × 71 × 31

#### Solution:

5 × 5 × 5 × 5 × 7 × 3
[Original expression.]

There are four 5's, one 7 and one 3 in the prime factorization.

= 54 × 71 × 31
[Write in exponential form.]

85.
Which of the following are twin primes?
 a. 2, 11 b. 3, 5 c. 7, 11 d. 2, 3

#### Solution:

Two prime numbers that differ by 2 are called twin primes.

The pairs of numbers (2, 3), (7, 11) and (2, 11) do not differ by two.

Prime numbers (3, 5) differ by 2.

3, 5 are twin primes.

86.
Which of the following pairs of numbers are twin primes?
 a. 31, 37 b. 41, 43 c. 47, 51 d. 41, 47

#### Solution:

Two prime numbers that differ by 2 are called twin primes.

The pair of numbers (31, 37), (41, 47) and (47, 51) do not differ by two.

Prime numbers 41, 43 differ by 2.

41, 43 are twin primes.

87.
Which of the following pair of prime numbers are not twin primes?
 a. 29, 31 b. 31, 37 c. 41, 43 d. 11, 13

#### Solution:

Two prime numbers that differ by 2 are called twin primes.

Prime numbers (29, 31), (11, 13) and (41, 43) differ by two.

Prime numbers 31 and 37 do not differ by 2.

31 and 37 are not twin primes.

88.
Identify the twin primes among the numbers from 10 to 20.
 a. 13, 19 b. 11, 13 and 17, 19 c. 13, 17 d. 11, 17

#### Solution:

Two prime numbers that differ by 2 are called twin primes.

The pair of numbers (13, 17), (11, 17) and (13, 19) do not differ by two.

The pairs of numbers (11, 13) and (17, 19) differ by 2.

(11, 13) and (17, 19) are two sets of twin primes.

89.
Which of the numbers from 50 to 60 are twin primes?
 a. 51, 53 b. 51, 57 c. 53, 59 d. None of the above

#### Solution:

Two prime numbers that differ by 2 are called twin primes.

The pair of numbers (53, 57), (51, 57) and (53, 59) do not differ by two.

Only the pair of numbers (51, 53) differs by 2. But 51 is not a prime number.

The correct choice for the question is 'D'