﻿ Prime Factorization Worksheets - Page 8 | Problems & Solutions # Prime Factorization Worksheets - Page 8

Prime Factorization Worksheets
• Page 8
71.
Which of the figures represent(s) the factor tree for 120?  a. figure 1 b. figure 2 c. figure 3 d. figures 1 & 2

#### Solution:

= 3 × 40
120
[Write 120 as a product of 3 and 40.]

= 3 × 2 × 20
[Write 40 as a product of 2 and 20.]

= 3 × 2 × 2 × 10
[Write 20 as a product of 2 and 10.]

= 3 × 2 × 2 × 2 × 5
[Write 10 as a product of 2 and 5.]

So, figure 3 represents the factor tree for 120.

72.
Find the cube root of 64 from the factor tree.  a. 8 b. 4 c. 6 d. 2

#### Solution:

From the factor tree, we can write 64 as 2 × 2 × 2 × 2 × 2 × 2.

(2 × 2 × 2) × (2 × 2 × 2)
[Write the product of three 2's as one group.]

2 × 2 = 4
[Select one 2 from each group and multiply.]

The cube root of 64 is 4.

73.
Using divisibility tests, state whether 50 is a prime or a composite number. a. Composite b. Prime

#### Solution:

The one's digit of 50 is 0.

A number is divisible by 2, if its one's digit is even and a number is divisible by 5 and 10, if its one's digit is 0.

50 is divisible by 2, 5 and 10.

A number that has factors other than 1 and itself is called a composite number.

50 is a composite number.

74.
Which of the numbers 3, 4, 12 or 15 has a prime factor greater than 3? a. 3 b. 15 c. 4 d. 12

#### Solution:

3 = 1 × 3
[Write the prime factorization of 3.]

4 = 2 × 2
[Write the prime factorization of 4.]

12 = 2 × 2 × 3
[Write the prime factorization of 12.]

15 = 3 × 5
[Write the prime factorization of 15.]

5 is a prime and greater than 3.

Only 15 has the prime factor greater than 3.

75.
Is 15 a prime or a composite number? a. Composite b. Prime c. Even prime d. Neither prime nor composite

#### Solution:

To find whether 15 is a prime or composite, draw the rectangles from exactly 15 squares. The following graph shows that two rectangles of dimensions 3 × 5 and 15 × 1 can be drawn from 15 squares.

The dimensions of the rectangle show that the factors of 15 are 1, 3, 5, and 15.

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

So, 15 is a composite number.

76.
Write the prime factorization of 3 × 2 × 3 × 7 using exponents. a. 32 × 22 × 71 b. 31 × 22 × 71 c. 32 × 21 × 71 d. 31 × 21 × 71

#### Solution:

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

3 × 2 × 3 × 7 = 32 × 21 × 71
[Factors in their exponential form.]

The prime factorization of 3 × 2 × 3 × 7 using exponents is 32 × 21 × 71

77.
Write the prime factorization of 5 × 2 × 2 using exponents. a. 51 × 22 b. 52 × 23 c. 52 × 21 d. 51 × 21

#### Solution:

5 × 2 × 2
[Original expression.]

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

= 51 × 22
[Factors in their exponential form.]

The prime factorization of 5 × 2 × 2 using exponents is 51 × 22.

78.
Find whether 47 is a prime or a composite number. a. Prime b. Composite

#### Solution:

The only divisors of 47 are 1 and 47.

If a number has exactly two factors, 1 and itself, then the number is called a prime number.

47 is a prime number.

79.
Write the prime factorization of 4 × 6 × 6 × 8 × 8 by using exponents. a. 41 × 63 × 82 b. 41 × 62 × 82 c. 42 × 62 × 82 d. 41 × 62 × 83

#### Solution:

4 × 6 × 6 × 8 × 8
[Original expression.]

There are one 4, two 6's and two 8's in the prime factorization.

= 41 × 62 × 82
[Factors in their exponential form.]

The prime factorization of 4 × 6 × 6 × 8 × 8 using exponents is 41 × 62 × 82.

80.
Write the prime factorization of 7 × 7 × 7 × 5 × 5 × 5 × 3 × 3 using exponents. a. 73 × 52 × 32 b. 73 × 53 × 33 c. 73 × 53 × 32 d. 72 × 53 × 32

#### Solution:

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

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

= 73 × 53 × 32
[Write in exponential form.]