# NCERT Solutions for Class 6 Maths Chapter 3 Exercise 3.2

NCERT Solutions for Class 6 Maths Chapter 3: NCERT Solutions for Class 6 Maths Chapter 3 Playing With Numbers Exercise 3.2

## NCERT Solutions for Class 6 Maths Chapter 3 Whole Numbers Exercise 3.2

1. What is the sum of any two
(A) Odd numbers?
(B) Even numbers?

Solution:

(A) The sum of any two odd numbers is an even number.
Example: 1+3=4,3+5=8

(B) The sum of any two even numbers is also an even number.
Example: 2+4=6,6+8=14

2. State whether the following statements are True or False:
(A) The sum of three odd numbers is even.
(B) The sum of two odd numbers and one even number is even.
(C) The product of three odd numbers is odd.
(D) If an even number is divided by 2, the quotient is always odd.
(E) All prime numbers are odd.
(F) Prime numbers do not have any factors.
(G) The Sum of two prime numbers is always even.
(H) 2 is the only even prime number.
(I) All even numbers are composite numbers.
(J) The product of two even numbers is always even.

Solution:

(A) False
For example, 1+3+5=9, which is an odd number.

(B) True
For example, 1+3+4=8, which is an even number.

(C) True
For example, 1×3×5=15, which is an odd number.

(D) False

We can see that both even and odd number appears as quotient.

(E) False
For example, 2 is an even prime number.

(F) False
Prime numbers have 1 and the number itself as factors.

(G) False
The Sum of two prime numbers can be even or odd.
For example, 2+5=7, 5+7=12

(H) True
The only even prime number is 2.

(I) False
Composite numbers have at least three factors whereas prime numbers have only two factors, 1 and the number itself.

(J) True
The product of two even numbers is always even because it has 2 as a common factor.

3. The numbers 13 and 31 are prime numbers. Both these numbers have same digits 1 and 𝟑. Find such pairs of prime numbers up to 100.

Solution:

Given, prime numbers like 13 and 31
So,
17 and 71;
37 and 73;
79 and 97 are three pairs.

4. Write down separately the prime and composite numbers less than 20.

Solution:

Prime numbers are those numbers which have only two factors 1 and the number itself.
Prime numbers: 2,3,5,7,11,13,17,19

Composite numbers are those numbers which have at least three factors.
Composite numbers: 4,6,8,9,10,12,14,15,16,18

5. What is the greatest prime number between 1 and 10?

Solution:

The greatest prime number between 1 and 10 is ‘7’.

6. Express the following as the sum of two odd primes.
(A) 44
(B) 36
(C) 24
(D) 18

Solution:

(A) 44=3+41
(B) 36=31+5
(C) 24=19+5
(D) 18=13+5

7. Give three pairs of prime numbers whose difference is 2.
[Remark: Two prime numbers whose difference is 2 are called twin primes].

Solution:

Following are the three pairs of twin primes: –
3 and 5;
5 and 7;
11 and 13

8. Which of the following numbers are prime?
(A) 23
(B) 51
(C) 37
(D) 26

Solution:

(A) 23 and (C) 37 are prime numbers.

9. Write seven consecutive composite numbers less than 100 so that there is no prime number between them.

Solution:

Seven consecutive composite numbers: 90,91,92,93,94,95,96

10. Express each of the following numbers as the sum of three odd primes:
(A) 21
(B) 31
(C) 53
(D) 61

Solution:

(A) 21=3+7+11
(B) 31=3+11+17
(C) 53=13+17+23
(D) 61=19+29+13

11. Write five pairs of prime numbers less than 20 whose sum is divisible by 5.(Hint:
3+7=10)

Solution:

2+3=5; 7+13=20; 3+17=20; 2+13=15; 5+5=10

12. Fill in the blanks:
(A) A number which has only two factors is called a ……………
(B) A number which has more than two factors is called a…………….. .
(C) 1 is neither _…………………. nor ……………….
(D) The smallest prime number is …………………..
(E) The smallest composite number is ……………………

Solution:

(A) Prime number
A prime number has only two factors 1 and the number itself.

(B) Composite number
A composite number has more than two factors.

(C) Prime number and composite number

(D) The smallest prime number is 2.

(E) Composite numbers have more than two factors. The smallest composite number is 4.