Factoring Word Problems

**Page 1**

1.

Find the greatest common factor of 19 and 4.

a. | 19 | ||

b. | 2 | ||

c. | 1 | ||

d. | 4 |

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 |

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 |

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 |

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 |

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 |

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 |

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 |

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 |

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 |

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)