Factoring Word Problems

**Page 5**

41.

Is 2 a factor of 296?

a. | No | ||

b. | Yes |

So, 2 is a factor of 296.

Correct answer : (2)

42.

Is 5 a factor of 704?

a. | Yes | ||

b. | No |

The number 704 ends with 4.

So, 5 is not a factor of 704.

Correct answer : (2)

43.

Is 6 a factor of 126?

a. | No | ||

b. | Yes |

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

Therefore it must also be divisible by 6.

So, 6 is a factor of 126.

Correct answer : (2)

44.

Which of the following numbers is not a factor of 880?

a. | 10 | ||

b. | 11 | ||

c. | 2 | ||

d. | 3 |

The number ends with 0, so it is divisible by 10.

So, it is also divisible by 88.

[10 × 88 = 880.]

The digits of the number 880 do not add up to 3 so it is not divisible by 3.

So, 3 is not a factor of 880.

Correct answer : (4)

45.

Which of the following numbers is a factor of 34?

a. | 4 | ||

b. | 2 | ||

c. | 5 | ||

d. | 3 |

The digits of 34 do not add up to a number which is divisible by 3, so the number itself is not divisible by 3.

The number 34 does not end with 0 or 5, so it is not divisible by 5.

The number 34 is not divisible by 4.

So, 2 is a factor of 34.

Correct answer : (2)

46.

Which of the following numbers is not a factor of 315?

a. | 6 | ||

b. | 5 | ||

c. | 9 | ||

d. | 3 |

The digits of the number add up to 9, so it is also divisible by 9.

Since the number ends with 5, it is divisible by 5.

The number 315 is not divisible by 6.

So, 6 is not a factor of 315.

Correct answer : (1)

47.

Which of the following numbers is not a factor of 18?

a. | 2 | ||

b. | 3 | ||

c. | 5 | ||

d. | 6 |

The digits of 18 add up to 9, so it is also divisible by 3.

Therefore it must also be divisible by 6.

The number 18 is not divisible by 5 as it does not end with 0 or 5.

So, 5 is not a factor of 18.

Correct answer : (3)

48.

Which of the following numbers is not a factor of 75?

a. | 7 | ||

b. | 5 | ||

c. | 3 | ||

d. | 15 |

Since the number ends with 5, it is divisible by 5.

Since the number is divisible by both 3 and 5, it is also divisible by 15.

The number 75 is not divisible by 7.

So, 7 is not a factor of 75.

Correct answer : (1)

49.

The factors of a number can be obtained through _______________ rules.

a. | Divisibility | ||

b. | Multiplication | ||

c. | Factorization | ||

d. | None of the above |

Correct answer : (1)

50.

Identify the factor pair of 18.

a. | 3, 9 | ||

b. | 1, 8 | ||

c. | 2, 9 | ||

d. | 2, 4 |

Since the number has the digits whose sum is divisible by 3, it is divisible by 3.

The sum of the digits is divisible by 9, so it is divisible by 9.

So, the factor pair of 18 is 2, 9.

Correct answer : (3)