Prime Factorization Worksheets

**Page 12**

111.

Using divisibility test, state whether 75 is a prime or a composite number.

a. | Composite | ||

b. | Prime |

[Use the divisibility test.]

So, 75 has more than two factors.

A whole number greater than 1 with more than two factors is called a composite number.

75 is a composite number.

Correct answer : (1)

112.

Using divisibility test, find whether 82 is a prime or a composite number.

a. | Prime | ||

b. | Composite |

Since the one's digit of the number 82 is even, 82 is divisible by 2. It has more than two factors.

[Use the divisibility test.]

A whole number greater than 1 with more than two factors is called a composite number.

82 is a composite number.

Correct answer : (2)

113.

Using divisibility test, find whether 54 is a prime or a composite number.

a. | Prime | ||

b. | Composite |

[Use the divisibility test.]

It has more than two factors.

A whole number greater than 1 with more than two factors is called a composite number.

54 is a composite number.

Correct answer : (2)

114.

Which of the numbers 18, 13, 11 and 19 is composite?

a. | 11 | ||

b. | 13 | ||

c. | 18 | ||

d. | 19 |

The only divisors of 13, 11 and 19 are 1 and the numbers themselves.

Since the sum of the digits of the number 18 is divisible by 3, 18 is divisible by 3. It has more than two factors.

[Use the divisibility test.]

Among the numbers, the number 18 is a composite number.

Correct answer : (3)

115.

Write the prime factorization of 256 in exponential form using a factor tree.

a. | 2 ^{5} | ||

b. | 2 ^{8} | ||

c. | 2 ^{7} | ||

d. | 2 ^{6} |

Write the number 256 as a product of two factors and factorize all the composite factors.

256 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2

The prime factorization of 256 is:

256 = 2

[Write in the exponential form.]

The prime factorization of 256 is 2

Correct answer : (2)

116.

Find the prime factorization of 325 using a factor tree.

a. | 5 ^{2} × 13^{1} | ||

b. | 5 ^{2} × 3^{1} | ||

c. | 5 ^{2} × 13^{2} | ||

d. | 5 ^{3} × 13^{1} |

Write the number 325 as a product of two factors and factorize the remaining composite factors.

The prime factors of 325 are: 325 = 5 × 5 × 13

325 = 5

[Write in the exponential form.]

The prime factorization of 325 is 5

Correct answer : (1)

117.

Find the prime factorization of 160 in exponential form using a factor tree.

a. | 2 ^{3} × 5^{1} | ||

b. | 2 ^{5} × 5^{2} | ||

c. | 2 ^{5} × 5^{1} | ||

d. | 2 ^{4} × 5^{1} |

Write the number 160 as a product of two factors and factorize the composite factors.

160 = 2 × 2 × 2 × 2 × 2 × 5

The prime factorization of 160 is:

160 = 2

[Write in the exponential form.]

The prime factorization of 160 is 2

Correct answer : (3)

118.

Express 18 as difference of two prime numbers.

a. | (29 - 11) | ||

b. | (31 - 13) | ||

c. | (30 - 12) | ||

d. | (28 - 10) |

18 can be expressed as a difference of two prime numbers in two ways, which is:29 - 11 = 18, 23 - 5 = 18 .

Among the choices, 18 is expressed as (29 - 11), which is the difference of two prime numbers.

Correct answer : (1)

119.

Which number in the set of numbers (2, 5, 9, 3) is a common factor among the prime factors of 4, 10 and 18?

a. | 5 | ||

b. | 2 | ||

c. | 9 | ||

d. | 3 |

The prime factors of 10 are: 10 = 5 x 2.

The prime factors of 18 are: 18 = 3 x 3 x 2.

In the set of numbers, the number 2 is a common factor among the prime factors of 4, 10 and 18.

Correct answer : (2)

120.

Find the product of all the prime factors of 16.

a. | 4 | ||

b. | 16 | ||

c. | 21 | ||

d. | 8 |

The product of all the prime factors of the number 16 is 16.

Correct answer : (2)