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Toggle## Class 6, Maths, Chapter 3, Exercise 3.2 Solutions

**Q.1. What is the sum of any two (a) Odd numbers? (b) Even numbers?**

**Ans:**

(i) Odd number = Number that cannot be divided by 2.

(ii) Even number = Number that can be divided by 2.

(a) The sum of any **two odd numbers is even** numbers.

Examples:

3 + 5 = 8,

7 + 3 =10,

15 + 17 = 32

(b) The sum of any **two even numbers is even** numbers

Examples:

4 + 8 = 12,

8 + 6 = 14,

16 + 16 = 32

**Q.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) 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.**

**Ans:**

**(a) False,** The sum of three odd numbers is odd.

**Explanation:** 3 + 5 + 7 = 15 i.e. odd number

**(b) True,** the sum of two odd numbers and one even numbers is even.

**Explanation: **3 + 5 + 8 = 16 i.e., even number.

**(c) True,** the product of three odd numbers is odd.

**Explanation: **3 × 5 × 7 = 105 i.e., odd number.

**(d) False,** if an even number is divided by 2, the quotient is even.

**Explanation: **8 ÷ 2 = 4 i.e., even number.

**(e) False,** all prime numbers are not odd.

**Explanation:** 2 is a prime number but it is also an even number.

**(f) False, **Prime numbers do have factors like 1 and the numbers itself are the factors of the numbers.

**(g) False,** Sum of two prime numbers may also be odd number

**Explanation: **2 + 3 = 5 i.e., odd number.

**(h) True,** 2 is the only even prime number.

**(i) False, **2 is the prime number.

**(j) True.** The product of two even numbers is always even.

**Explanation:** 2 × 4 = 8 i.e., even number.

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

**Ans: ****Let’s know what is the prime number:**

A prime number is a number that is only divisible by 1 and by the number itself.

The prime numbers with same digits upto 100 are:

17 and 71

37 and 73

79 and 97

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

**Ans:**

**Prime number:** A prime number is a number that is only divisible by 1 and by the number itself.

In other words, Prime numbers are the numbers that has only two factors: 1 and number itself

**Composite number: **A composite number has more than two factors. For example, 4 is a composite number because it can be factored as 2 x 2.

**Remember: **Every Number that is not a prime number is a composite number.

**(a) Prime numbers:** 2, 3, 5, 7, 11, 13, 17 and 19 are the prime numbers less than 20

**(b) Composite numbers:** 4, 6, 8, 9, 10, 12, 14, 15, 16 and 18 are the composite numbers less than 20.

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

**Ans: **

The greatest prime number between 1 and 10 is 7.

The prime numbers between 1 and 10 are: 2, 3, 5, 7. Out of these, 7 is the greatest prime number.

**Q.6. Express the following as the sum of two odd primes.**

**(a) 44 **

**(b) 36 **

**(c) 24 **

**(d) 18**

**Ans:**

**(a) **3 + 41 = 44

(b) 5 + 31 = 36

(c) 7 + 17 = 24

(d) 3 + 15 = 18

**Q.7. Give three pairs of prime numbers whose difference is 2.**

**[Note: Two prime numbers whose difference is 2 are called twin primes].**

**Ans:**

The three pairs of prime numbers whose difference is 2 are

(3, 5): The difference between 3 and 5 is 2.

(5, 7): The difference between 5 and 7 is 2.

(11, 13): The difference between 11 and 13 is 2.

**Q.8. Which of the following numbers are prime?**

**(a) 23 **

**(b) 51 **

**(c) 37 **

**(d) 26**

** **

**Ans: **

**(a) 23 and (c) 37**

**Explanation: **

**(a) ****23**

1 × 23 = 23

23 × 1 = 23

∴ 23 has only two factors 1 and 23. Hence, it is a prime number.

**(c) 37**

1 × 37 = 37

37 × 1 = 37

∴ 37 has two factors 1 and 37. Hence, it is a prime number.

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

**Ans:**

Seven composite numbers between 89 and 97 both which are prime numbers are 90, 91, 92, 93, 94, 95 and 96.

**Q.10. Express each of the following numbers as the sum of three odd primes:**

**(a) 21 **

**(b) 31 **

**(c) 53 **

**(d) 61**

**Ans:**

**(a) **3 + 7 + 11 = 21

(b) 5 + 7 + 19 = 31

(c) 13 + 17 + 23= 53

(d) 13 + 17 + 31 = 61

**Q.11. Write five pairs of prime numbers less than 20 whose sum is divisible by 5.**

**(Hint: 3 +7 = 10)**

**Ans:**

The five pairs of prime numbers less than 20 whose sum is divisible by 5 are

2 + 3 = 5

5 + 5 = 10

2 + 13 = 15

3 + 17 = 20

7 + 13 = 20

**Q.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 _____.**

**(f) The smallest even number is ______.**

**Ans:**

**(a) **A number which has only two factors is called a ** prime number**.

(b) A number which has more than two factors is called a ** composite number**.

(c) 1 is neither ** prime number** nor

**.**

*composite number*(d) The smallest prime number is *2.*

(e) The smallest composite number is *4.*

(f) The smallest even number is **2.**

## NCERT Solutions For Class 6 Maths, Chapter 3 Playing With Numbers (All Exercises)

**Class 6, Maths, Chapter 3, Playing With Numbers **

**Class 6, Maths, Chapter 3, Playing With Numbers, Exercise 3.1**

**Class 6, Maths, Chapter 3, Playing With Numbers, Exercise 3.2** **← You are here**

**Class 6, Maths, Chapter 3, Playing With Numbers, Exercise 3.3**

**Class 6, Maths, Chapter 3, Playing With Numbers, Exercise 3.4**

**Class 6, Maths, Chapter 3, Playing With Numbers, Exercise 3.5**

**Class 6, Maths, Chapter 3, Playing With Numbers, Exercise 3.6**

**Class 6, Maths, Chapter 3, Playing With Numbers, Exercise 3.7**