Prime Factorization Worksheets

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131.

The prime factorization of a number 676 is given by 2^{$a$} × 13^{$b$}. What are the values of $a$ and $b$?

a. | 2 and 2 | ||

b. | 1 and 2 | ||

c. | 2 and 1 | ||

d. | none of the above |

The prime factorization of 676 = 2 x 2 x 13 x 13.

2 x 2 x 13 x 13 = 2

[Convert product form to exponential form.]

So, the values of

Correct answer : (1)

132.

The prime factorization of 99 is given by 3 × __ × __. What are the missing values?

a. | 6 and 11 | ||

b. | 3 and 11 | ||

c. | 2 and 11 | ||

d. | none of the above |

The prime factorization of 99 = 3 x 3 x 11.

The missing terms in the expression 3 x __ x __ are 3 and 11.

Correct answer : (2)

133.

Is 3 a prime or a composite number?

a. | Prime | ||

b. | Composite | ||

c. | Both prime and composite | ||

d. | Neither prime nor composite |

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

To find whether 3 is a prime number or composite, draw the rectangles that can be made from exactly 3 squares.

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

So, 3 is a prime number.

Correct answer : (1)

134.

Is 16 a prime or a composite number?

a. | Prime | ||

b. | Composite | ||

c. | Neither prime nor composite |

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

To find whether 16 is a prime number or composite, draw the rectangles that can be made from exactly 16 squares.

The dimensions of the rectangle show that the factors of 16 are 1, 2, 4, 8 and 16.

The number 16 has 5 factors.

So, 16 is a composite number.

Correct answer : (2)

135.

Find the prime factorization of 96.

a. | 3 ^{2} × 2^{4} | ||

b. | 3 ^{1} × 2^{3} | ||

c. | 3 ^{1} × 2^{5} | ||

d. | 3 ^{2} × 2^{5} |

The factor tree of 96 is:

[96 = 24 × 4, 24 = 6 × 4, 4 = 2 × 2, 6 = 3 × 2]

The circled numbers in the factor tree are the prime factors of 96.

96 = 3 × 2 × 2 × 2 × 2 × 2

Correct answer : (3)

136.

What is a prime number?

a. | Number having only two factors, other than one and itself. | ||

b. | Number having more than two factors. | ||

c. | Number having two factors, one and itself. | ||

d. | None of the above |

Correct answer : (3)

137.

What is a composite number?

a. | Number having only two factors. | ||

b. | Number having more than two factors. | ||

c. | Number having two factors, one and itself. | ||

d. | None of the above |

Correct answer : (2)

138.

List all the prime numbers, which are less than 10.

a. | 2, 3, 5 and 7 | ||

b. | 2, 3, 4 and 7 | ||

c. | 2, 4, 5 and 7 | ||

d. | 3, 5, 7 |

Prime numbers less than 10 are 2, 3, 5 and 7.

Correct answer : (1)

139.

List all the prime numbers, which are greater than 20 and less than 30.

a. | 23 and 29 | ||

b. | 23 and 27 | ||

c. | 27 and 29 | ||

d. | 23, 27, 29 |

List of prime numbers greater than 20 and less than 30 are 23 and 29.

Correct answer : (1)

140.

Is 1 a prime number or a composite number?

a. | Prime | ||

b. | Composite | ||

c. | Both prime and composite | ||

d. | Neither prime nor composite |

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

1 is neither a prime nor a composite number.

Correct answer : (4)