﻿ Prime and Composite Numbers Worksheet - Page 2 | Problems & Solutions

Prime and Composite Numbers Worksheet - Page 2

Prime and Composite Numbers Worksheet
• Page 2
11.
Which of these is a prime number?
 a. 31 b. 27 c. 39 d. 45

Solution:

A number whose factors are 1 and the number itself, is called a prime number.

In the given choices, 27, 45, and 39 have factors other than 1 and itself.

Factors of 31 are 1 and 31.

So, 31 is a prime number.

12.
Identify the prime number.
 a. 47 b. 9 c. 38 d. 50

Solution:

A number whose factors are 1 and the number itself, is called a prime number.

In the given choices, 9, 38, and 50 have factors other than 1 and itself.

Factors of 47 are 1 and 47.

So, 47 is a prime number.

13.
Write whether the number 2 is prime or composite.
 a. Composite b. Prime

Solution:

To list the factors of 2, draw rectangular arrays that have a total of 2 squares.

From the figure, 1 × 2 = 2.

So, the factors of 2 are 1 and 2.

So, 2 is a prime number.
[A prime number has exactly two factors, 1 and itself.]

14.
Write whether the number 14 is prime or composite.
 a. Composite b. Prime

Solution:

To list the factors of 14, draw rectangular arrays that have a total of 14 squares.

From the figure, 1 × 14 = 14 and 2 × 7 = 14.

So, the factors of 14 are 1, 2, 7 and 14.

So, 14 is a composite number.
[A composite number has more than two factors.]

15.
Say whether the number 19 is prime or composite.
 a. composite b. prime

Solution:

The number 19 can be factorized as 1 × 19.

Its factors are 1 and 19.

The number 19 has only two factors showing one rectangular array.

So, the number 19 is prime.

16.
Which set of numbers represents all the prime numbers between 6 and 21?
 a. 7, 9, 11, 13, 17, 19 b. 6, 8, 10, 12, 14, 16, 18 c. 7, 11, 13, 17 d. 7, 11, 13, 17, 19

Solution:

A prime number has exactly two factors, 1 and itself.

The numbers with exactly two factors between 6 and 21 are 7, 11, 13, 17 and 19.

So, 7, 11, 13, 17, 19 represent the set of numbers with all the prime numbers between 6 and 21.

17.
Which set of numbers represents all the composite numbers between 31 and 43?
 a. 31, 33, 34, 35, 36, 37, 39, 40, 43 b. 32, 33, 34, 35, 36, 38, 39, 40, 42 c. 32, 33, 34, 35, 36, 37, 39, 41, 42 d. None of the above

Solution:

A composite number has more than two factors.

The numbers with more than two factors between 31 and 43 are 32, 33, 34, 35, 36, 38, 39, 40 and 42.

So, 32, 33, 34, 35, 36, 38, 39, 40, 42 represent the set of numbers with all the composite numbers between 31 and 43.

18.
Are there more prime numbers between 24 and 37 than those between 34 and 45?
 a. Yes b. No

Solution:

A prime number has exactly two factors, 1 and itself.

The numbers with exactly two factors between 24 and 37 are 29 and 31.

The numbers with exactly two factors between 34 and 45 are 37, 41, and 43.

The number of prime numbers between 24 and 37 is lesser than the number of prime numbers between 34 and 45.
[The number of prime numbers between 24 and 37 is 2 and the number of prime numbers between 34 and 45 is 3.]

So, the number of prime numbers between 24 and 37 is not more than the number of prime numbers between 34 and 45.

19.
The numbers ____ and ____ are neither prime nor composite.
 a. 0 and 3 b. 0 and 1 c. 1 and 9 d. 1 and 2

Solution:

The numbers 0 and 1 are neither prime nor composite.