Worksheet on Prime Number

Special numbers divisible only by themselves fascinate mathematical minds. Children discover prime number printable practice questions that explore the unique properties of numbers like 2, 3, 5, 7, and beyond through engaging detective work. These intriguing activities help students identify prime characteristics while understanding their importance in cryptography and mathematics. Students can download the prime number free worksheet PDF. Every prime number reveals mathematical elegance and mystery.

1. Which of the following pairs of numbers is co-prime?

a) 14 and 35
b) 15 and 28
c) 21 and 49
d) 22 and 44

Answer: b)

Explanation: Two numbers are co-prime if they do not have any common factor other than 1.
15 and 28 do not have any common factors except 1.

Hence, 15 and 28 are co-prime.

2. If the least common multiple (LCM) of two numbers is 84 and their highest common factor (HCF) is 2, which of the following can be the numbers?

a) 21 and 49
b) 22 and 44
c) 14 and 12
d) 14 and 80

Answer: d)

Explanation: Let two numbers be a and b
Using the relation:
LCM x HCF = Product of two numbers
84 x 2 = a x b
168 = a x b

Only 14 and 12 satisfy the above condition.

3. Consider the following statements:

I. All prime numbers are odd numbers.
II.  There are only five single-digit prime numbers
III. There are infinitely many prime numbers.
IV. A prime number has only two factors.

Which of the above statements are true?

a) I and II
b) II and IV
c) III and IV
d) II, III and IV

Answer: c)

Explanation: I. All prime numbers are odd numbers.
2 is a prime number, which is an even number. Thus, false.
II. There are only five single-digit prime numbers.
There are not 5 single-digit numbers, but only 4 single-digit prime numbers such as 2, 3, 5 and 7. Thus, false.
III. There are infinitely many prime numbers.
There are an infinite number of natural numbers. So there will be infinitely many prime numbers. Thus, true.
IV. A prime number has only two factors.
A prime number has only two factors, 1 and itself. Thus, true.

4. How many prime numbers are there between 100 and 120?

a) 5
b) 6
c) 7
d) 4

Answer: a)

Explanation: We know that prime numbers have only 2 factors, 1 and number itself. So, the prime numbers between 100 and 120 are: 101, 103, 107, 109 and 113.

5. A two-digit number, 9A, is a prime number. Find A.

a) 3
b) 1
c) 7
d) 9

Answer: c)

Explanation: The only prime number between 90 and 99 is 97. So one place digit would be 7.
Hence, A is 7.

6. Find the sum of all prime numbers between 60 and 100.

a) 492
b) 620
c) 420
d) 464

Answer: b)

Explanation: The prime numbers between 60 and 100 are: 61, 67, 71, 73, 79, 83, 89 and 97.
The sum of these prime numbers is:
61 + 67 + 71 + 73 + 79 + 83 + 89 + 97 = 620

Hence, the sum of all prime numbers between 60 and 100 is 620.

7. How many prime numbers are there between 1 and 50?

a) 7
b) 13
c) 12
d) 15

Answer: d)

Explanation: The prime numbers between 1 and 50 are:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47
There are 15 prime numbers in total, between 1 and 50.

8. How many distinct prime factors does 210 have?

a) 3
b) 4
c) 5
d) 6

Answer: b)

Explanation: The prime factors of 210 are 2, 3, 5, and 7. There are 4 distinct prime factors.

9. If the product of two co-prime numbers is 221, what is their sum?

a) 30
b) 22
c) 23
d) 24

Answer: a)

Explanation: Co-prime pairs that multiply to 221: 13 and 17.
Sum = 13 + 17 = 30.

10. If the sum of the reciprocals of two distinct prime numbers is 20/91, what are the prime numbers?

a) 3 and 5
b) 3 and 7
c) 5 and 11
d) 7 and 13

Answer: d)

Explanation: Let the primes be p and q. Then, $\frac{\frac{1}{}}{\frac{p}{}}$ + $\frac{\frac{1}{}}{\frac{q}{}}$ = $\frac{\frac{\mathrm{p\; +\; q}}{}}{\frac{\mathrm{pq}}{}}$ = $\frac{\frac{\mathrm{20}}{}}{\frac{\mathrm{91}}{}}$
Only p = 7 and q = 13 satisfy the above condition.

Hence, the required prime numbers are 7 and 13.