#### Solved Examples and Worksheet for Prime and Composite Numbers

Q1Find the prime numbers upto 36.
A. 2,3,5,7,11,13,17,19,23,29,31
B. 2,3,5,7,11,13,17
C. 2,3,5,7
D. 2,3,5,7,11,13,17,19,23
E. 2,3,5,7,11,13,17,19,23,29,31,36

Step: 1
Prime numbers upto 36 = 2,3,5,7,11,13,17,19,23,29,31.
Q2Identify the composite number.

A. 29
B. 19
C. 48
D. 47

Step: 1
A composite number is a number which has at least one factor
other than 1 and itself.
So, it is not a prime number.
Step: 2
In the given choices, 47, 19 and 29 are prime numbers.
Step: 3
48 has factors 1, 2, 3, 4, 6, 8,12, 16 and 48.
Step: 4
Thus, 48 has factors other than 1 and 48.
Step: 5
So, 48 is a composite number.
Q3Which set of numbers represents all the composite numbers between 15 and 25?
A. 16, 18, 20, 21, 22, 23, 25
B. 16, 18, 20, 21, 22, 24
C. 16, 18, 19, 22,24
D. 16, 19, 20, 22, 24

Step: 1
A composite number has more than two factors.
Step: 2
The numbers BETWEEN 15 and 25 with more than two factors are 16, 18, 20, 21, 22 and 24.
Step: 3
So, 16, 18, 20, 21, 22, 24 represent the set of numbers with all the composite numbers between 15 and 25.
Correct Answer is :   16, 18, 20, 21, 22, 24
Q4Identify the number that has more than two factors.
A. 37
B. 51
C. 41
D. 31

Step: 1
A composite number is a number which has more than two factors.
Step: 2
Factors of 31 are 1 and 31.
Step: 3
Factors of 41 are 1 and 41.
Step: 4
Factors of 37 are 1 and 37.
Step: 5
Factors of 51 are 1, 3, 17, and 51.
Step: 6
Among the choices, the number that has more than two factors is 51.
Q5Identify a composite number.

A. 35
B. 71
C. 113
D. 59

Step: 1
A composite number has more than two factors.
Step: 2
Factors of 59 : 1, and 59
Factors of 71 : 1 and 71
Factors of 113 : 1 and 113
Factors of 35 : 1, 5, 7, and 35
Step: 3
The number 35 has more than two factors.
Step: 4
So, the number 35 is a composite number.
Q6Identify the composite number.
A. 28
B. 59
C. 71

Step: 1
A number that has more than two factors is called a composite number.
Step: 2
Factors of 59 = 1, 59
Step: 3
Factors of 71 = 1, 71
Step: 4
Factors of 28 = 1, 2, 4, 7,14, 28.
Step: 5
Out of the given numbers, 28 is the only number that has more than two factors.
Step: 6
So, 28 is the composite number.
Q7Which set of numbers represents all the prime numbers between 2 and 30?

A. 3, 5, 7, 11, 13, 17, 19, 23 and 29
B. 2, 3, 5, 7, 11, 13, 17, 19, 23 and 29
C. 2, 3, 4, 5, 7, 11, 13, 15, 17, 19, 23 and 29
D. 1, 2, 3, 5, 7, 11, 13, 17, 19, 23 and 29

Step: 1
A prime number is a whole number that is divisible only by itself and the number 1.
Step: 2
3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29
[List of odd numbers between 2 and 30.]
Step: 3
3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29
[Apart from 3, 5 and 7, strike out the numbers divisible by 3, 5 and 7.]
Step: 4
Hence, all the prime numbers between 2 and 30 are 3, 5, 7, 11, 13, 17, 19, 23 and 29.
Correct Answer is :   3, 5, 7, 11, 13, 17, 19, 23 and 29
Q8Determine the largest prime number that is less than 38.

A. 39
B. 37
C. 29
D. 31

Step: 1
A prime number is a whole number that is divisible only by itself and the number 1.
Step: 2
The prime numbers that are less than 38 are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31 and 37.
Step: 3
The largest prime number that is less than 38 is 37.
Q9Which of the following is not a prime number?
A. 36
B. 11
C. 13
D. 17

Step: 1
A prime number is a whole number that is divisible only by itself and the number 1.
Step: 2
11 ÷ 2 = 5 remainder 1, 11 ÷ 3 = 3 remainder 2
Step: 3
13 ÷ 2 = 6 remainder 1, 13 ÷ 3 = 4 remainder 1
Step: 4
17 ÷ 2 = 8 remainder 1, 17 ÷ 3 = 5 remainder 2
Step: 5
36 ÷ 2 = 18
Step: 6
The numbers 11, 13 and 17 are prime numbers.
Step: 7
So, 36 is not a prime number.
Q10Which set of numbers represents all the prime numbers between 9 and 21?
A. 9, 11, 13, 17 and 19
B. 10, 12, 14, 16 and 18
C. 11, 13 and 17
D. 11, 13, 17 and 19

Step: 1
A prime number is a whole number that is divisible only by itself and the number 1.
Step: 2
11, 13, 15, 17, 19
[List of odd numbers between 9 and 21.]
Step: 3
11, 13, 15, 17, 19
[Strike out the numbers divisible by 3, 5 and 7.]
Step: 4
Hence, all the prime numbers between 9 and 21 are 11, 13, 17 and 19.
Correct Answer is :   11, 13, 17 and 19
Q11Which of the following is a composite number ?

A. 113
B. 59
C. 20
D. 71

Step: 1
A number that has more than two factors is called a composite number.
Step: 2
Factors of 59 = 1, 59
Step: 3
Factors of 71 = 1, 71
Step: 4
Factors of 113 = 1, 113
Step: 5
Factors of 20 = 1, 2, 4, 5, 10, 20
Step: 6
Out of the given numbers, 20 is the only number that has more than two factors.
Step: 7
So, 20 is the composite number.
Q12Which of these is a composite number?
A. 73
B. 83
C. 53
D. 93

Step: 1
A number that has more than two factors is called a composite number.
Step: 2
Factors of 53 = 1, 53
Step: 3
Factors of 73 = 1, 73
Step: 4
Factors of 83 = 1, 83
Step: 5
Factors of 93 = 1, 3, 31, 93
Step: 6
Out of the given numbers, 93 is the only number that has more than two factors.
Step: 7
So, 93 is the composite number.
Q13Which of these is a composite number?

A. 37
B. 5
C. 15
D. 43

Step: 1
A number that has more than two factors is called a composite number.
Step: 2
Factors of 5 = 1, 5
Step: 3
Factors of 37 = 1, 37
Step: 4
Factors of 43 = 1, 43
Step: 5
Factors of 15 = 1, 3, 5, 15
Step: 6
Out of the given numbers, 15 is the only number that has more than two factors.
Step: 7
So, 15 is the composite number.
Q14Which of these is a prime number?

A. 51
B. 91
C. 71
D. 81

Step: 1
A number whose factors are 1 and the number itself, is called a prime number.
Step: 2
In the given choices, 51, 81, and 91 have factors other than 1 and itself.
Step: 3
Factors of 71 are 1 and 71.
Step: 4
So, 71 is a prime number.
Q15Which of these is a prime number?

A. 39
B. 99
C. 29
D. 69

Step: 1
A number whose factors are 1 and the number itself, is called a prime number.
Step: 2
In the given choices, 39, 69, and 99 have factors other than 1 and itself.
Step: 3
Factors of 29 are 1 and 29.
Step: 4
So, 29 is a prime number.