Prime Factorization Worksheets

**Page 8**

71.

Which of the figures represent(s) the factor tree for 120?

a. | figure 1 | ||

b. | figure 2 | ||

c. | figure 3 | ||

d. | figures 1 & 2 |

120

[Write 120 as a product of 3 and 40.]

= 3 × 2 × 20

[Write 40 as a product of 2 and 20.]

= 3 × 2 × 2 × 10

[Write 20 as a product of 2 and 10.]

= 3 × 2 × 2 × 2 × 5

[Write 10 as a product of 2 and 5.]

So, figure 3 represents the factor tree for 120.

Correct answer : (3)

72.

Find the cube root of 64 from the factor tree.

a. | 8 | ||

b. | 4 | ||

c. | 6 | ||

d. | 2 |

(2 × 2 × 2) × (2 × 2 × 2)

[Write the product of three 2's as one group.]

2 × 2 = 4

[Select one 2 from each group and multiply.]

The cube root of 64 is 4.

Correct answer : (2)

73.

Using divisibility tests, state whether 50 is a prime or a composite number.

a. | Composite | ||

b. | Prime |

A number is divisible by 2, if its one's digit is even and a number is divisible by 5 and 10, if its one's digit is 0.

50 is divisible by 2, 5 and 10.

A number that has factors other than 1 and itself is called a composite number.

50 is a composite number.

Correct answer : (1)

74.

Which of the numbers 3, 4, 12 or 15 has a prime factor greater than 3?

a. | 3 | ||

b. | 15 | ||

c. | 4 | ||

d. | 12 |

[Write the prime factorization of 3.]

4 = 2 × 2

[Write the prime factorization of 4.]

12 = 2 × 2 × 3

[Write the prime factorization of 12.]

15 = 3 × 5

[Write the prime factorization of 15.]

5 is a prime and greater than 3.

Only 15 has the prime factor greater than 3.

Correct answer : (2)

75.

Is 15 a prime or a composite number?

a. | Composite | ||

b. | Prime | ||

c. | Even prime | ||

d. | Neither prime nor composite |

The following graph shows that two rectangles of dimensions 3 × 5 and 15 × 1 can be drawn from 15 squares.

The dimensions of the rectangle show that the factors of 15 are 1, 3, 5, and 15.

A number that has more than two factors is called a composite number.

So, 15 is a composite number.

Correct answer : (1)

76.

Write the prime factorization of 3 × 2 × 3 × 7 using exponents.

a. | 3 ^{2} × 2^{2} × 7^{1} | ||

b. | 3 ^{1} × 2^{2} × 7^{1} | ||

c. | 3 ^{2} × 2^{1} × 7^{1} | ||

d. | 3 ^{1} × 2^{1} × 7^{1} |

3 × 2 × 3 × 7 = 3

[Factors in their exponential form.]

The prime factorization of 3 × 2 × 3 × 7 using exponents is 3

Correct answer : (3)

77.

Write the prime factorization of 5 × 2 × 2 using exponents.

a. | 5 ^{1} × 2^{2} | ||

b. | 5 ^{2} × 2^{3} | ||

c. | 5 ^{2} × 2^{1} | ||

d. | 5 ^{1} × 2^{1} |

[Original expression.]

The prime factorization has one 5 and two 2's.

= 5

[Factors in their exponential form.]

The prime factorization of 5 × 2 × 2 using exponents is 5

Correct answer : (1)

78.

Find whether 47 is a prime or a composite number.

a. | Prime | ||

b. | Composite |

If a number has exactly two factors, 1 and itself, then the number is called a prime number.

47 is a prime number.

Correct answer : (1)

79.

Write the prime factorization of 4 × 6 × 6 × 8 × 8 by using exponents.

a. | 4 ^{1} × 6^{3} × 8^{2} | ||

b. | 4 ^{1} × 6^{2} × 8^{2} | ||

c. | 4 ^{2} × 6^{2} × 8^{2} | ||

d. | 4 ^{1} × 6^{2} × 8^{3} |

[Original expression.]

There are one 4, two 6's and two 8's in the prime factorization.

= 4

[Factors in their exponential form.]

The prime factorization of 4 × 6 × 6 × 8 × 8 using exponents is 4

Correct answer : (2)

80.

Write the prime factorization of 7 × 7 × 7 × 5 × 5 × 5 × 3 × 3 using exponents.

a. | 7 ^{3} × 5^{2} × 3^{2} | ||

b. | 7 ^{3} × 5^{3} × 3^{3} | ||

c. | 7 ^{3} × 5^{3} × 3^{2} | ||

d. | 7 ^{2} × 5^{3} × 3^{2} |

[Original expression.]

There are three 7's, three 5's and two 3's in the prime factorization.

= 7

[Write in exponential form.]

Correct answer : (3)