﻿ Factoring Word Problems | Problems & Solutions Factoring Word Problems

Factoring Word Problems
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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.

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.

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.

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.

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.

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.

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.

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.

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.

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.