Factoring Word Problems

**Page 3**

21.

Choose all the factors of 6.

a. | 3, 2 | ||

b. | 1, 2, 3, 6 | ||

c. | 1, 2, 3 | ||

d. | 6, 12, 18 |

It is also divisible by 3.

So, the factors of 6 are 1, 2, 3, 6.

Correct answer : (2)

22.

Which of the given expressions is equivalent to 3 × 6?

a. | 3 × 5 | ||

b. | 7 × 4 | ||

c. | 9 × 2 | ||

d. | 3 × 4 |

[6 = 3 × 2.]

= 9 × 2

So, 9 × 2 is the same as 3 × 6.

Correct answer : (3)

23.

14 × 7 = 98. Identify the option that would give you the same product.

a. | 2 × 6 × 7 | ||

b. | 2 × 7 × 7 | ||

c. | 2 × 7 × 9 | ||

d. | 3 × 4 × 2 |

[Original expression.]

14 × 7 = 2 × 7 × 7

So, 2 × 7 × 7 gives the same product as 14 × 7.

Correct answer : (2)

24.

Identify another way of writing the product 6 × 5.

a. | 3 × 3 × 4 | ||

b. | 2 × 4 × 5 | ||

c. | 2 × 3 × 5 | ||

d. | 3 × 3 × 5 |

[Original expression.]

6 × 5 = 2 × 3 × 5

So, 2 × 3 × 5 is another way of writing the product of 6 × 5.

Correct answer : (3)

25.

Identify the expression that is equivalent to 3 × 10.

a. | 3 × 5 | ||

b. | 15 × 1 | ||

c. | 3 × 6 | ||

d. | 6 × 5 |

3 × 10 = (3 × 2) × 5

= 6 × 5

So, 6 × 5 is the same as 3 × 10.

Correct answer : (4)

26.

2 × 6 = 12. Which of the given expressions has a product equal to 12?

a. | 3 × 11 | ||

b. | 7 × 3 | ||

c. | 9 × 2 | ||

d. | 4 × 3 |

[Original expression.]

2 × 6 = (2 × 2) × 3

[6 = 2 × 3.]

= 4 × 3 = 12

So, 4 × 3 is equal to 12.

Correct answer : (4)

27.

The prime factorization of a number is 2^{2} × 3^{2} × 5^{2} . Identify the number.

a. | 900 | ||

b. | 800 | ||

c. | 1,000 | ||

d. | 700 |

= 900

2

Correct answer : (1)

28.

Choose a rectangle that shows the factors of 21.

a. | Figure 1 | ||

b. | Figure 2 | ||

c. | Figure 4 | ||

d. | Figure 3 |

Figure 1 shows a rectangle with 21 squares.

So, Figure 1 represents the rectangle that shows the factors of 21.

Correct answer : (1)

29.

Choose a rectangle that shows the factors of 16.

a. | Figure 3 | ||

b. | Figure 2 | ||

c. | Figure 4 | ||

d. | Figure 1 |

Figure 2 shows a rectangle with 16 squares.

So, Figure 2 represents the rectangle that shows the factors of 16.

Correct answer : (2)

30.

Do the numbers 8 and 11 have a factor in common?

a. | Yes | ||

b. | No |

The rectangle(s) showing the factors of 8 is given as:

Factors of 8: 1, 2, 4, 8

[Since 1 × 8 = 8 and 2 × 4 = 8.]

The rectangles showing the factors of 11 is given as:

Factors of 11: 1, 11

[Since 1 × 11 = 11.]

So, the numbers 8 and 11 do not have a factor in common.

Correct answer : (2)