Prime Factorization Worksheets

**Page 6**

51.

Identify the prime number.

a. | 57 | ||

b. | 9 | ||

c. | 13 | ||

d. | 33 |

Correct answer : (3)

52.

Which of the following is the prime factorization of 54?

a. | 3 × 2 × 8 | ||

b. | 2 × 2 × 11 | ||

c. | 3 × 2 × 3 × 3 | ||

d. | 3 × 2 × 9 |

Correct answer : (3)

53.

Which of the following represents 8 × 8?

a. | 2 ^{8} | ||

b. | 8 ^{3} | ||

c. | 8(2) | ||

d. | 8 ^{2} |

Correct answer : (4)

54.

What is the prime factorization of 768?

a. | 2 ^{7} × 3^{1} | ||

b. | 2 ^{8} × 3^{1} | ||

c. | 2 ^{2} × 5^{3} | ||

d. | 2 ^{3} × 3^{1} × 5^{4} |

Correct answer : (2)

55.

Find the missing number in the factor tree.

a. | 5 | ||

b. | 4 | ||

c. | 3 | ||

d. | 2 |

[Express 27 as a multiple of 9.]

The missing number in the factor tree is 3.

Correct answer : (3)

56.

A rectangle can be formed in two different ways using exactly 18 squares as shown in the figure. Find the factors of 18 excluding 1 and itself.

a. | 5, 6 and 9 | ||

b. | 2, 3, 6 and 9 | ||

c. | 1, 3, 6 and 18 | ||

d. | None of the above |

So, the factors of 18 are 2, 3, 6 and 9.

Correct answer : (2)

57.

Find the square root of 144.

a. | 14 | ||

b. | 22 | ||

c. | 24 | ||

d. | 12 |

Draw the factor tree for 144 as shown in the figure.

From the factor tree, we can write 144 as 2 × 2 × 3 × 3 × 2 × 2 = 2

The square root of 144 is 2 × 2 × 3 = 12.

[Take two 2's and one 3 out of the four 2's and two 3's and multiply.]

Correct answer : (4)

58.

Using the factor tree, find the prime factors of 760.

a. | 4, 5, 5 and 19 | ||

b. | 2, 2, 2, 5 and 19 | ||

c. | 2, 3, 5, 5 and 19 | ||

d. | 2, 10, 5 and 19 |

So, the prime factorization of 760 = 2 × 2 × 2 × 5 × 19.

Correct answer : (2)

59.

Select a model for representing the factor tree for 360.

a. | Figure 3 | ||

b. | Figure 1 | ||

c. | Figure 4 | ||

d. | Figure 1 and Figure 2 |

[Select the prime factors from figure 1 and multiply.]

2 x 5 x 2 x 2 x 3 x 3 = 360

[Select the prime factors from figure 2 and multiply.]

3 x 3 x 2 x 2 = 36

[Select the prime factors from figure 3 and multiply.]

3 x 3 x 7 x 2 x 2 = 252

[Select the prime factors from figure 4 and multiply.]

In both figure 1 and figure 2, the product of the prime numbers is 360.

So, figure 1 and figure 2 are the models that represent the factor tree for 360.

Correct answer : (4)

60.

Find the G.C.F of 24 and 32, using the factor trees.

a. | 3 | ||

b. | 4 | ||

c. | 6 | ||

d. | 8 |

Both 24 and 32 have the common factors 2 x 2 x 2.

The product of the common factors is 2 x 2 x 2 = 8.

The G.C.F of 24 and 32 is 8.

Correct answer : (4)