NCERT Solutions For Class 6 Maths Chapter 3

Playing With Numbers

NCERT Solutions For Class 6 Maths Chapter 3 Exercise 3.2

Exercise 3.1 Exercise 3.3 Exercise 3.4 Exercise 3.5 Exercise 3.6 Exercise 3.7

Question 1:

What is the sum of any two
(a) Odd numbers
(b) Even numbers

Answer 1:

(a) The sum of any two odd numbers is even numbers.
Examples: 5 + 7 = 12 , 17 + 15 = 32
(b) The sum of any two even numbers is even numbers
Examples: 4 + 6 = 10 , 14 + 34 = 48

Question 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.

Answer 2:

(a) False. Ex 3 + 5 + 7 = 15i.e odd number
(b) True. EX: 7 + 9 + 8 = 24 i.e is even number.
(c) True. Ex: 3 × 5 × 7 = 105 i.e is odd number.
(d) False. Ex: 10 ÷ 2 = 5 is even.
(e) False, Ex: 2 is a prime number but it is also an even number.
(f) False.
(g) False. Ex: 2 + 7 = 9 i.e odd number.
(h) True. 2 is the only even prime number.
(i) False. 2 is a prime number.
(j) True. Ex: 6 × 4 = 24 i.e even number.

Question 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.

Answer 3:

The paire of prime numbers with same digits upto 100 are as follows:
17 and 71 37 and 73, 79 and 97

Question 4

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

Answer 4:

These numbers 2, 3, 5, 7, 11, 13, 17 and 19 are the prime numbers less than 20
These numbers 4, 6, 8, 9, 10, 12, 14, 15, 16 and 18 are the composite numbers less than 20

Question 5

What is the greatest prime number between 1 and 10?

Answer 5:

The prime number between 1 and 10 are 2,5 and 7
So, 7 is the greatest prime number between 1 and 10.

Question 5:

Express the following as the sum of two odd primes.
(a) 44
(b) 36
(c) 24
(d) 18

Answer 5:

(a) 3 + 41 = 44
(b) 5 + 31 = 36
(c) 5 + 19 = 24
(d) 5 + 13 = 18

Question 6:

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

Answer 6:

3 and 5 5 and 7 11 and 13

Question 7

Which of the following numbers are prime? (a) 23
(b) 51
(c) 37
(d) 26

Answer 7:

(a) 23
1 × 23 = 23
23 × 1 = 23
prime numbers
(b) 51
1 × 51 = 51
3 × 17 = 51
not a prime numbers
(c) 37
1 × 37 = 37
37 × 1 = 37
prime numbers
(d) 26
1 × 26 = 26
2 × 13 = 26
not a prime numbers

Therefore a) 27 and c) 37 are prime numbers

Question 8

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

Answer 8:

90
91
92
93
94
95
96

Factors
1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90
1, 7, 13, 91
1, 2, 4, 23, 46, 92
1, 3, 31, 93
1, 2, 47, 94
1, 5, 19, 95
1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96

Seven composite numbers are 90, 91, 92, 93, 94, 95 and 96

Question 9

Express each of the following numbers as the sum of three odd primes:
(a) 21
(b) 31
(c) 53
(d) 61

Answer 9:

(a) 3 + 5 + 13 = 21
(b) 5+ 7 + 19 = 31
(c) 13 + 17 + 23= 53
(d) 7 + 17 + 37 = 61

Question 10:

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

Answer 10:

The five pairs of prime numbers less than 20 whose sum is divisible by 5 are 5=2 + 3
15=2 + 13
20=3 + 17
20=7 + 13
30 =19 + 11

Question 11

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 ______.