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 |

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 |

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 |

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 |

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 |

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 |

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 |

So, 3 is a factor of 27.

Correct answer : (3)

38.

Is 5 a factor of 50?

a. | No | ||

b. | Yes |

So, 5 is a factor of 50.

Correct answer : (2)

39.

Is 6 a factor of 63?

a. | No | ||

b. | Yes |

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 |

So, 20 is a factor of 140.

Correct answer : (2)