﻿ Prime Factorization Worksheets - Page 7 | Problems & Solutions

# Prime Factorization Worksheets - Page 7

Prime Factorization Worksheets
• Page 7
61.
Using the factor tree, find the cube root of 729.

 a. 6 b. 7 c. 8 d. 9

#### Solution:

From the factor tree, the prime factorization of 729 is 3 × 3 × 3 × 3 × 3 × 3.

(3 × 3 × 3 × 3 × 3 × 3)1/3 = 3 × 3
[Take the cube root of the factors of 729.]

3 × 3 = 9
[Multiply.]

The cube root of 729 is 9.

62.
Choose the factor tree for 24.

 a. Figure - 1 b. Figure - 2 c. Figure - 3 d. Figure - 1 & Figure - 2

#### Solution:

The factor tree is used to find a number's prime factors. So, the leaves of a factor tree should be prime numbers.

= 3 × 8
24
[Using prime factorization.]

= 3 × 2 × 4

= 3 × 2 × 2 × 2

So, Figure - 1 is the factor tree of 24.

63.
Find the values of $a$, $b$ and $c$ in the factor tree.

 a. 54, 2, 9 b. 36, 3, 6 c. 36, 3, 15 d. 21, 2, 6

#### Solution:

From the factor tree, a = 3 × 18 = 54
[Multiply 3 and 18.]

From the factor tree, 18 = b × c

18 = 2 × 9 = 3 × 6
[Express 18 as the product of two numbers.]

The values of a, b and c are 54, 2 and 9.

64.
Which two factor trees model the same number?

 a. Figure - 2 & Figure - 4 b. Figure - 1 & Figure - 4 c. Figure - 1 & Figure - 2 d. Figure - 1 & Figure - 3

#### Solution:

In Figure - 1, the number in the box at the second level from the top of the tree = 2 × 2 = 4.

The number at the top of the tree = 16 × 4 = 64.

In Figure - 2, the number in the box at the second level of the tree from top = 5 × 3 = 15.

The number at the top of the tree = 5 × 15 = 75.

In Figure - 3, the number in the box at the second level from the top of the tree = 2 × 4 = 8.

The number at the top of the tree = 8 × 8 = 64.

In Figure - 4, the number at the top of the tree = 13 × 4 = 52.

The factor trees in Figure - 1 & Figure - 3 model the same number 64.

65.
Identify the factor trees that model prime factorization of the number.

 a. Figure 1 b. Figure 2 c. Figure 3 d. Figure 1 and Figure 2

#### Solution:

In Figure 1, 2 and 3 are prime numbers and 4 is not a prime number.

So, Figure 1 does not model the prime factorization of 24.

In Figure 2, 2 and 13 are prime numbers.

So, Figure 2 models the prime factorization of 52.

In Figure 3, 2 is a prime number and 4 is not a prime number.

So, Figure 3 does not model the prime factorization of 32.

Only Figure 2 models the prime factorization of the number.

66.
Find the cube root of 216 from the factor tree.

 a. 18 b. 6 c. 24 d. 12

#### Solution:

From the factor tree, 216 = 2 × 2 × 2 × 3 × 3 × 3 = 23 × 33.

The cube root of 216 = 2 × 3 = 6
[Get one 2 out of three 2's and one 3 out of three 3's and multiply.]

67.
Find the square root of 81 from the factor tree.

 a. 27 b. 81 c. 9 d. 3

#### Solution:

From the factor tree, 81 = 3 × 3 × 3 × 3 = 32 × 32.

The square root of 81 = 3 × 3 = 9.
[Get two 3's out of four and multiply.]

68.
Using the factor tree, find the quotient obtained when 216 is divided by 27.

 a. 4 b. 3 c. 9 d. 8

#### Solution:

From the factor tree, 216 = 8 × 27.

The quotient obtained when 216 divided by 27 is 8.

69.
What are the values of $a$, $b$ and $c$ in the factor tree?

 a. 16, 2, 2 b. 16, 2, 4 c. 16, 2, 3 d. None of the above

#### Solution:

From the factor tree, a = 2 × 8 = 16
[Multiply 2 and 8.]

From the factor tree, 8 = b × 4.

8 = 2 × 4
[Express 8 as a multiple of 4.]

So, b = 2.

From the factor tree, 4 = c × 2.

4 = 2 × 2
[Express 4 as a multiple of 2.]

So, c = 2.

The values of a, b and c are 16, 2 and 2.

70.
Find the prime factorization of 8 using the factor tree.
 a. 2 × 2 × 2 b. 8 × 1 c. 2 × 6 d. 2 × 4

#### Solution:

Since 2 is a prime number, the prime factorization of 8 = 2 × 2 × 2.