The **NCERT Solutions For Class 6 Maths Chapter 3 Playing with Numbers Exercise 3.2** is the continuation of the 1st exercise of the chapter.Â In the previous exercise, we have learnt about the factors and multiples. Now, in this exercise ofÂ **NCERT Class 6 Maths Chapter 3,** we get a brief idea about the prime and composite numbers. We, at BYJUâ€™S, have provided NCERT Solutions for the students to aid them in understanding the steps involved in solving the problems. The numbers which have factors as 1 and the number itself are prime numbers and those having many factors are composite numbers. Learn more about prime and composite numbers by practising theÂ NCERT Solutions of Class 6 MathsÂ that is being provided here for the second exercise of Chapter 3 Playing with Numbers.

## NCERT Solutions for Class 6 Chapter 3: Playing with Numbers Exercise 3.2 Download PDF

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### Access NCERT Solutions for Class 6 Chapter 3: Playing with Numbers Exercise 3.2

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

**Solutions:**

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

Examples: 5 + 3 = 8

15 + 13 = 28

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

Examples: 2 + 8 = 10

12 + 28 = 40

**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.**

**Solutions:**

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

Example: 7 + 9 + 5 = 21 i.e odd number

(b) True. The sum of two odd numbers and one even numbers is even.

Example: 3 + 5 + 8 = 16 i.e is even number.

(c) True. The product of three odd numbers is odd.

Example: 3 Ã— 7 Ã— 9 = 189 i.e is odd number.

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

Example: 8 Ã· 2 = 4

(e) False, All prime numbers are not odd.

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

(f) False. Since, 1 and the number itself are factors of the number

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

Example: 2 + 5 = 7 i.e odd number.

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

(i) False. Since, 2 is a prime number.

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

Example: 2 Ã— 4 = 8 i.e even number.

**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.**

**Solutions:**

The prime numbers with same digits upto 100 are as follows:

17 and 71

37 and 73

79 and 97

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

**Solutions:**

2, 3, 5, 7, 11, 13, 17 and 19 are the prime numbers less than 20

4, 6, 8, 9, 10, 12, 14, 15, 16 and 18 are the composite numbers less than 20

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

**Solutions:**

2, 3, 5 and 7 are the prime numbers between 1 and 10. 7 is the greatest prime number among them.

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

**(a) 44 **

**(b) 36 **

**(c) 24 **

**(d) 18**

**Solutions:**

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

(b) 5 + 31 = 36

(c) 5 + 19 = 24

(d) 5 + 13 = 18

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

**Solutions:**

The three pairs of prime numbers whose difference is 2 are

3, 5

5, 7

11, 13

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

**(a) 23 **

**(b) 51 **

**(c) 37 **

**(d) 26**

**Solutions:**

(a) 23

1 Ã— 23 = 23

23 Ã— 1 = 23

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

(b) 51

1 Ã— 51 = 51

3 Ã— 17 = 51

Therefore 51 has four factors 1, 3, 17 and 51. Hence, it is not a prime number, it is a composite number.

(c) 37

1 Ã— 37 = 37

37 Ã— 1 = 37

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

(d) 26

1 Ã— 26 = 26

2 Ã— 13 = 26

Therefore 26 has four factors 1, 2, 13 and 26. Hence, it is not a prime number, it is a composite number.

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

**Solutions:**

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

NumbersÂ Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Factors

90Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90

91Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 1, 7, 13, 91

92Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 1, 2, 4, 23, 46, 92

93Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 1, 3, 31, 93

94Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 1, 2, 47, 94

95Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 1, 5, 19, 95

96Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96

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

**(a) 21 **

**(b) 31 **

**(c) 53 **

**(d) 61**

**Solutions:**

**(a) **3 + 5 + 13 = 21

(b) 3 + 5 + 23 = 31

(c) 13 + 17 + 23= 53

(d) 7 + 13 + 41 = 61

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

**Solutions:**

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

2 + 3 = 5

2 + 13 = 15

3 + 17 = 20

7 + 13 = 20

19 + 11 = 30

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**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 ______.**

**Solutions:**

**(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.