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# Factoring Word Problems

Factoring Word Problems
• Page 1
1.
Find the greatest common factor of 19 and 4.
 a. 19 b. 2 c. 1 d. 4

#### Solution:

List all the factors of the numbers.
Factors of 19: 1 and 19
Factors of 4: 1, 2 and 4

Select the common factors:
Factors of 19: 1 and 19
Factors of 4: 1, 2 and 4

Since 1 is the only common factor of 19 and 4, the greatest common factor of 19 and 4 is 1.

Correct answer : (3)
2.
Find the greatest common factor of 16 and 26.
 a. 8 b. 2 c. 9 d. 4

#### Solution:

List all the factors of the numbers
Factors of 16: 1, 2, 4, 8 and 16
Factors of 26: 1, 2, 13 and 26

Select the common factors
Factors of 16: 1, 2, 4, 8 and 16
Factors of 26: 1, 2, 13 and 26

Among the common factors 1 and 2, the greatest common factor is 2.

Therefore, the greatest common factor of 16 and 26 is 2.

Correct answer : (2)
3.
Find the greatest common factor of 7 and 21.
 a. 21 b. 1 c. 7 d. 3

#### Solution:

List all the factors of the numbers.
Factors of 7: 1 and 7
Factors of 21: 1, 3, 7 and 21

Select the common factors.
Factors of 7: 1 and 7
Factors of 21: 1, 3, 7 and 21

Among the common factors 1 and 7, the greatest common factor is 7.

Therefore, the greatest common factor of 7 and 21 is 7.

Correct answer : (3)
4.
Find the greatest common factor of 13 and 27.
 a. 3 b. 1 c. 27 d. 13

#### Solution:

List all the factors of the numbers.
Factors of 13: 1 and 13
Factors of 27: 1, 3, 9 and 27

Select the common factors.
Factors of 13: 1 and 13
Factors of 27: 1, 3, 9 and 27

Since 1 is the only common factor of 13 and 27, the greatest common factor of 13 and 27 is 1.

Correct answer : (2)
5.
Find the greatest common factor of 15 and 20.
 a. 5 b. 6 c. 3 d. 8

#### Solution:

List all the factors of the numbers.
Factors of 15: 1, 3, 5 and 15
Factors of 20: 1, 2, 4, 5, 10 and 20

Select all the common factors.
Factors of 15: 1, 3, 5 and 15
Factors of 20: 1, 2, 4, 5, 10 and 20

Among the common factors 1 and 5, the grestest common factor is 5.

Therefore, the greatest common factor of 15 and 20 is 5.

Correct answer : (1)
6.
Find the greatest common factor of 16 and 18.
 a. 2 b. 4 c. 1 d. 6

#### Solution:

List all the factors of the numbers
Factors of 16: 1, 2, 4, 8 and 16
Factors of 18: 1, 2, 3, 6, 9 and 18.

List all the factors of the numbers
Factors of 16: 1, 2, 4, 8 and 16
Factors of 18: 1, 2, 3, 6, 9 and 18.

Among the common factors 1 and 2, the greatest common factor is 2.

Therefore, the greatest common factor of 16 and 18 is 2.

Correct answer : (1)
7.
Find the greatest common factor of 11 and 33.
 a. 33 b. 11 c. 44 d. 22

#### Solution:

List all the factors of the numbers.
Factors of 11: 1 and 11
Factors of 33: 1, 3, 11 and 33

Select all the common factors.
Factors of 11: 1 and 11
Factors of 33: 1, 3, 11 and 33

Among the common factors 1 and 11, the greatest common factor is 11.

Therefore, the greatest common factor of 11 and 33 is 11.

Correct answer : (2)
8.
Find the greatest common factor of 19 and 30.
 a. 1 b. 9 c. 7 d. 5

#### Solution:

List all the factors of the numbers.
Factors of 19: 1, 19
Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30

Select the common factors.
Factors of 19: 1, 19
Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30

Since 1 is the only common factor of 19 and 30, the greatest common factor of 19 and 30 is 1.

Correct answer : (1)
9.
Find the greatest common factor of 28 and 32.
 a. 4 b. 1 c. 8 d. 9

#### Solution:

List all the factors of the numbers.
Factors of 28: 1, 2, 4, 7, 14 and 28
Factors of 32: 1, 2, 4, 8, 16 and 32

Select the common factors.
Factors of 28: 1, 2, 4, 7, 14 and 28
Factors of 32: 1, 2, 4, 8, 16 and 32

Among the common factors 1, 2 and 4, the greatest common factor is 4.

Therefore, the greatest common factor of 28 and 32 is 4.

Correct answer : (1)
10.
Find the greatest common factor of 40 and 48.
 a. 4 b. 2 c. 8 d. 5

#### Solution:

List all the factors of the numbers.
Factors of 40: 1, 2, 4, 5, 8, 10, 20 and 40
Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48.

Select the common factors.
Factors of 40: 1, 2, 4, 5, 8, 10, 20 and 40.
Factors of 48: 1, 2, 4, 6, 8, 12, 16, 24 and 48

Among the common factors 1, 2, 4 and 8, the greatest common factor is 8.

Therefore, the greatest common factor of 40 and 48 is 8.

Correct answer : (3)

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