Prime Factorization Worksheets

**Page 7**

61.

Using the factor tree, find the cube root of 729.

a. | 6 | ||

b. | 7 | ||

c. | 8 | ||

d. | 9 |

(3 × 3 × 3 × 3 × 3 × 3)

[Take the cube root of the factors of 729.]

3 × 3 = 9

[Multiply.]

The cube root of 729 is 9.

Correct answer : (4)

62.

Choose the factor tree for 24.

a. | Figure - 1 | ||

b. | Figure - 2 | ||

c. | Figure - 3 | ||

d. | Figure - 1 & Figure - 2 |

= 3 × 8

24

[Using prime factorization.]

= 3 × 2 × 4

= 3 × 2 × 2 × 2

So, Figure - 1 is the factor tree of 24.

Correct answer : (1)

63.

Find the values of $a$, $b$ and $c$ in the factor tree.

a. | 54, 2, 9 | ||

b. | 36, 3, 6 | ||

c. | 36, 3, 15 | ||

d. | 21, 2, 6 |

[Multiply 3 and 18.]

From the factor tree, 18 =

18 = 2 × 9 = 3 × 6

[Express 18 as the product of two numbers.]

The values of

Correct answer : (1)

64.

Which two factor trees model the same number?

a. | Figure - 2 & Figure - 4 | ||

b. | Figure - 1 & Figure - 4 | ||

c. | Figure - 1 & Figure - 2 | ||

d. | Figure - 1 & Figure - 3 |

The number at the top of the tree = 16 × 4 = 64.

In Figure - 2, the number in the box at the second level of the tree from top = 5 × 3 = 15.

The number at the top of the tree = 5 × 15 = 75.

In Figure - 3, the number in the box at the second level from the top of the tree = 2 × 4 = 8.

The number at the top of the tree = 8 × 8 = 64.

In Figure - 4, the number at the top of the tree = 13 × 4 = 52.

The factor trees in Figure - 1 & Figure - 3 model the same number 64.

Correct answer : (4)

65.

Identify the factor trees that model prime factorization of the number.

a. | Figure 1 | ||

b. | Figure 2 | ||

c. | Figure 3 | ||

d. | Figure 1 and Figure 2 |

So, Figure 1 does not model the prime factorization of 24.

In Figure 2, 2 and 13 are prime numbers.

So, Figure 2 models the prime factorization of 52.

In Figure 3, 2 is a prime number and 4 is not a prime number.

So, Figure 3 does not model the prime factorization of 32.

Only Figure 2 models the prime factorization of the number.

Correct answer : (2)

66.

Find the cube root of 216 from the factor tree.

a. | 18 | ||

b. | 6 | ||

c. | 24 | ||

d. | 12 |

The cube root of 216 = 2 × 3 = 6

[Get one 2 out of three 2's and one 3 out of three 3's and multiply.]

Correct answer : (2)

67.

Find the square root of 81 from the factor tree.

a. | 27 | ||

b. | 81 | ||

c. | 9 | ||

d. | 3 |

The square root of 81 = 3 × 3 = 9.

[Get two 3's out of four and multiply.]

Correct answer : (3)

68.

Using the factor tree, find the quotient obtained when 216 is divided by 27.

a. | 4 | ||

b. | 3 | ||

c. | 9 | ||

d. | 8 |

The quotient obtained when 216 divided by 27 is 8.

Correct answer : (4)

69.

What are the values of $a$, $b$ and $c$ in the factor tree?

a. | 16, 2, 2 | ||

b. | 16, 2, 4 | ||

c. | 16, 2, 3 | ||

d. | None of the above |

[Multiply 2 and 8.]

From the factor tree, 8 =

8 = 2 × 4

[Express 8 as a multiple of 4.]

So,

From the factor tree, 4 =

4 = 2 × 2

[Express 4 as a multiple of 2.]

So,

The values of

Correct answer : (1)

70.

Find the prime factorization of 8 using the factor tree.

a. | 2 × 2 × 2 | ||

b. | 8 × 1 | ||

c. | 2 × 6 | ||

d. | 2 × 4 |

Since 2 is a prime number, the prime factorization of 8 = 2 × 2 × 2.

Correct answer : (1)