﻿ Prime Factorization Worksheets - Page 6 | Problems & Solutions # Prime Factorization Worksheets - Page 6

Prime Factorization Worksheets
• Page 6
51.
Identify the prime number. a. 57 b. 9 c. 13 d. 33

52.
Which of the following is the prime factorization of 54? a. 3 × 2 × 8 b. 2 × 2 × 11 c. 3 × 2 × 3 × 3 d. 3 × 2 × 9

53.
Which of the following represents 8 × 8? a. 28 b. 83 c. 8(2) d. 82

54.
What is the prime factorization of 768? a. 27 × 31 b. 28 × 31 c. 22 × 53 d. 23 × 31 × 54

55.
Find the missing number in the factor tree.  a. 5 b. 4 c. 3 d. 2

#### Solution:

27 = 3 × 9
[Express 27 as a multiple of 9.]

The missing number in the factor tree is 3.

56.
A rectangle can be formed in two different ways using exactly 18 squares as shown in the figure. Find the factors of 18 excluding 1 and itself.  a. 5, 6 and 9 b. 2, 3, 6 and 9 c. 1, 3, 6 and 18 d. None of the above

#### Solution:

The dimensions of the two rectangles are 2 × 9 and 3 × 6.

So, the factors of 18 are 2, 3, 6 and 9.

57.
Find the square root of 144. a. 14 b. 22 c. 24 d. 12

#### Solution: Draw the factor tree for 144 as shown in the figure.

From the factor tree, we can write 144 as 2 × 2 × 3 × 3 × 2 × 2 = 24 × 32.

The square root of 144 is 2 × 2 × 3 = 12.
[Take two 2's and one 3 out of the four 2's and two 3's and multiply.]

58.
Using the factor tree, find the prime factors of 760.  a. 4, 5, 5 and 19 b. 2, 2, 2, 5 and 19 c. 2, 3, 5, 5 and 19 d. 2, 10, 5 and 19

#### Solution:

From the factor tree, 2, 5 and 19 are the prime numbers.

So, the prime factorization of 760 = 2 × 2 × 2 × 5 × 19.

59.
Select a model for representing the factor tree for 360.  a. Figure 3 b. Figure 1 c. Figure 4 d. Figure 1 and Figure 2

#### Solution:

5 x 2 x 2 x 2 x 3 x 3 = 360
[Select the prime factors from figure 1 and multiply.]

2 x 5 x 2 x 2 x 3 x 3 = 360
[Select the prime factors from figure 2 and multiply.]

3 x 3 x 2 x 2 = 36
[Select the prime factors from figure 3 and multiply.]

3 x 3 x 7 x 2 x 2 = 252
[Select the prime factors from figure 4 and multiply.]

In both figure 1 and figure 2, the product of the prime numbers is 360.

So, figure 1 and figure 2 are the models that represent the factor tree for 360.

60.
Find the G.C.F of 24 and 32, using the factor trees.  a. 3 b. 4 c. 6 d. 8

#### Solution:

From the factor trees, the prime factorization of 24 is 2 x 2 x 2 x 3 and 32 is 2 x 2 x 2 x 2 x 2.

Both 24 and 32 have the common factors 2 x 2 x 2.

The product of the common factors is 2 x 2 x 2 = 8.

The G.C.F of 24 and 32 is 8.