Prime Factorization Worksheets - Page 14

Prime Factorization Worksheets
• Page 14
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

Solution:

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

2 x 2 x 13 x 13 = 22 x 132
[Convert product form to exponential form.]

So, the values of a and b are 2 and 2.

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

Solution:

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

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

133.
Is 3 a prime or a composite number?
 a. Prime b. Composite c. Both prime and composite d. Neither prime nor composite

Solution:

A number that has exactly two factors, 1 and itself is called a prime number.

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.

134.
Is 16 a prime or a composite number?
 a. Prime b. Composite c. Neither prime nor composite

Solution:

A number that has exactly two factors, 1 and itself is called a prime number.

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.

135.
Find the prime factorization of 96.
 a. 32 × 24 b. 31 × 23 c. 31 × 25 d. 32 × 25

Solution:

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

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

Solution:

A number that has only two factors, one and itself is called a prime number.

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

Solution:

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

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

Solution:

A number that has only two factors, one and itself is called a prime number.

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

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

Solution:

A number that has only two factors, one and itself is called a prime number.

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

140.
Is 1 a prime number or a composite number?
 a. Prime b. Composite c. Both prime and composite d. Neither prime nor composite

Solution:

A number that has exactly two factors, 1 and itself is called a prime number.

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

1 is neither a prime nor a composite number.