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Factoring Word Problems
• Page 4
31.
What are the factors that the numbers 4 and 16 have in common? a. 2, 4 b. 3, 6 c. 2, 3 d. 2, 6

#### Solution: To list the factors of 4, draw rectangular arrays that have a total of 4 squares.

From the figure, 1 × 4 = 4 and 2 × 2 = 4.

So, the factors of 4 are 1, 2, 4. To list the factors of 16, draw rectangular arrays that have a total of 16 squares.

From the figure, 1 × 16 = 16, 2 × 8 = 16 and 4 × 4 = 16.

So, the factors of 16 are 1, 2, 4, 8 and 16.

So, the factors that 4 and 16 have in common are 2 and 4.

Correct answer : (1)
32.
Find the prime factors of 45 using factor trees. a. 2 × 2 × 2 b. 7 × 2 × 2 c. 5 × 3 × 3 d. 5 × 2 × 2

#### Solution: A factor tree written for 45 as the product of prime factors is:

Correct answer : (3)
33.
Which of the following shows the factors of 30? a. 30 = 5 × 5 × 2 b. 30 = 5 × 3 × 3 c. 30 = 5 × 2 × 2 d. 30 = 5 × 3 × 2

#### Solution:

The number 30 can be written as 5 × 6.

5 × 6 = 5 × 3 × 2
[Rewrite 6.]

So, the factors of 30 can be given as, 30 = 5 × 3 × 2.

Correct answer : (4)
34.
Choose all the factors of 8. a. 4, 2 b. 1, 2, 4, 8 c. 8, 16, 24 d. 1, 2, 3

#### Solution:

The number 8 is an even number, so it is divisible by 2.

It is also divisible by 4.

So, the factors of 8 are 1, 2, 4, 8.

Correct answer : (2)
35.
Choose the factors of 20. a. 1, 2, 4, 5, 10, 20 b. 1, 2, 3, 4, 5, 6 c. 1, 3, 6, 10 d. 1, 2, 3, 4, 8, 10

#### Solution:

The number 20 ends with the digit 0, so it is divisible by 5.

So, the factors of 20 are 1, 2, 4, 5, 10, 20.

Correct answer : (1)
36.
Select the factors of 15. a. 1, 3, 5, 15 b. 1, 2, 4, 15 c. 1, 2, 3, 4 d. 1, 3, 5, 10

#### Solution:

The number 15 has digits whose sum is divisible by 3, so it is divisible by 3.

The number ends with 5, it is also divisible by 5.

So, the factors of 15 are 1, 3, 5, 15.

Correct answer : (1)
37.
Which of the following numbers is a factor of 27? a. 4 b. 8 c. 3 d. 12

#### Solution:

The number 27 has digits whose sum is divisible by 3, it is divisible by 3.

So, 3 is a factor of 27.

Correct answer : (3)
38.
Is 5 a factor of 50? a. No b. Yes

#### Solution:

The number 50 ends with 0, so it is divisible by 5.

So, 5 is a factor of 50.

Correct answer : (2)
39.
Is 6 a factor of 63? a. No b. Yes

#### Solution:

The number 63 has digits whose sum is divisible by 3, so it is divisible by 3.

The number is not an even number so it is not divisible by 2, therefore it is not divisible by 6.

So, 6 is not a factor of 63.

Correct answer : (1)
40.
Is 20 a factor of 140? a. No b. Yes

#### Solution:

The number 140 ends in 0 and is also even, so it is divisible by 2 and 10, which are the factor pairs of 20.

So, 20 is a factor of 140.

Correct answer : (2)

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