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Factoring Word Problems
• Page 3
21.
Choose all the factors of 6. a. 3, 2 b. 1, 2, 3, 6 c. 1, 2, 3 d. 6, 12, 18

#### Solution:

The number 6 is an even number, so it is divisible by 2.

It is also divisible by 3.

So, the factors of 6 are 1, 2, 3, 6.

Correct answer : (2)
22.
Which of the given expressions is equivalent to 3 × 6? a. 3 × 5 b. 7 × 4 c. 9 × 2 d. 3 × 4

#### Solution:

3 × 6 = (3 × 3) × 2
[6 = 3 × 2.]

= 9 × 2

So, 9 × 2 is the same as 3 × 6.

Correct answer : (3)
23.
14 × 7 = 98. Identify the option that would give you the same product. a. 2 × 6 × 7 b. 2 × 7 × 7 c. 2 × 7 × 9 d. 3 × 4 × 2

#### Solution:

14 × 7 = 98
[Original expression.]

14 × 7 = 2 × 7 × 7

So, 2 × 7 × 7 gives the same product as 14 × 7.

Correct answer : (2)
24.
Identify another way of writing the product 6 × 5. a. 3 × 3 × 4 b. 2 × 4 × 5 c. 2 × 3 × 5 d. 3 × 3 × 5

#### Solution:

6 × 5
[Original expression.]

6 × 5 = 2 × 3 × 5

So, 2 × 3 × 5 is another way of writing the product of 6 × 5.

Correct answer : (3)
25.
Identify the expression that is equivalent to 3 × 10. a. 3 × 5 b. 15 × 1 c. 3 × 6 d. 6 × 5

#### Solution:

10 = 2 × 5

3 × 10 = (3 × 2) × 5

= 6 × 5

So, 6 × 5 is the same as 3 × 10.

Correct answer : (4)
26.
2 × 6 = 12. Which of the given expressions has a product equal to 12? a. 3 × 11 b. 7 × 3 c. 9 × 2 d. 4 × 3

#### Solution:

12 = 2 × 6
[Original expression.]

2 × 6 = (2 × 2) × 3
[6 = 2 × 3.]

= 4 × 3 = 12

So, 4 × 3 is equal to 12.

Correct answer : (4)
27.
The prime factorization of a number is 22 × 32 × 52. Identify the number. a. 900 b. 800 c. 1,000 d. 700

#### Solution:

22 × 32 × 52 = 2 × 2 × 3 × 3 × 5 × 5

= 900

22 × 32 × 52 = 900

Correct answer : (1)
28.
Choose a rectangle that shows the factors of 21.  a. Figure 1 b. Figure 2 c. Figure 4 d. Figure 3

#### Solution:

To list the factors of 21, draw rectangles that have a total of 21 squares.

Figure 1 shows a rectangle with 21 squares.

So, Figure 1 represents the rectangle that shows the factors of 21.

Correct answer : (1)
29.
Choose a rectangle that shows the factors of 16.  a. Figure 3 b. Figure 2 c. Figure 4 d. Figure 1

#### Solution:

To list the factors of 16, draw rectangles that have a total of 16 squares.

Figure 2 shows a rectangle with 16 squares.

So, Figure 2 represents the rectangle that shows the factors of 16.

Correct answer : (2)
30.
Do the numbers 8 and 11 have a factor in common? a. Yes b. No

#### Solution: The rectangle(s) showing the factors of 8 is given as:

Factors of 8: 1, 2, 4, 8
[Since 1 × 8 = 8 and 2 × 4 = 8.] The rectangles showing the factors of 11 is given as:

Factors of 11: 1, 11
[Since 1 × 11 = 11.]

So, the numbers 8 and 11 do not have a factor in common.

Correct answer : (2)

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