# Class 6 Chapter 3 Playing with Numbers

## Ncert Solution Class 6th Maths Chapter 3

Class 6 Chapter 3 Playing with Numbers | Ncert Solutions for Class 6 Maths Chapter 3 Playing with Numbers by Online Shiksha

### Chapter 3 Playing with Numbers – Exercise 3.1

#### 1. Write all the factors of the following numbers:

(a) 24 (b) 15 (c) 21 (d) 27 (e) 12 (f) 20 (g) 18 (h) 23 (i) 36

A product is obtained by multiplying two whole numbers. The multiplied numbers are the product’s factors. A factor, on the other hand, completely divides a number without leaving any remainder.

• Factors of 24 = 1, 2, 3, 4, 6, 12, 24
• Factors of 15 = 1, 3, 5, 15
• Factors of 21 = 1, 3, 7, 21
• Factors of 27 = 1, 3, 9, 27
• Factors of 12 = 1, 2, 3, 4, 6, 12
• Factors of 20 = 1, 2, 4, 5, 10, 20
• Factors of 18 = 1, 2, 3, 6, 9, 18
• Factors of 23 = 1, 23
• Factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36

#### 2. Write first five multiples of:  (a) 5 (b) 8 (c) 9

Multiples – Multiples are the results of multiplying a number by an integer.

• First five multiples of 5 are 5, 10, 15, 20, 25.
• First five multiples of 8 are 8, 16, 24, 32, 40.
• First five multiples of 9 are 9, 18, 27, 36, 45.

#### 3. Match the items in column 1 with the items in column 2:

 Column 1 Column 2 (i) 35 (a) Multiple of 8 (ii) 15 (b) Multiple of 7 (iii) 16 (c) Multiple of 70 (iv) 20 (d) Factor of 30 (v) 25 (e) Factor of 50 (f) Factor of 20

I – b , ii – d , iii – a , iv – f , v – e

#### Multiples of 9 up to 100 – 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99

9*1=9 , 9*2 = 18 , 9*3 = 27 , 9*4 = 36 ,9*5=45 , 9*6=54 , 9*7 =63 ,9*8 = 72 ,9*9 = 81 , 9*10=90 , 9*11 = 99

### Chapter 3 Playing with Numbers – Exercise 3.2

What is the sum of any two –

 Odd numbers. The sum of any two odd numbers is an even number. Example: 1 + 3 = 4, 3 + 5 = 8, 5+7= 12 , 7+9 = 16 , 9+11 = 20 , 11+13=14 ans so on….. Even numbers. The sum of any two even numbers is an even number. Example: 2 + 4 = 6, 4+6 = 10 , 6 + 8 = 14 , 8+10=18 , 10+12=22 , 12+14 = 26 and so on………..

State whether the following statements are true or false-

 The sum of three odd numbers is even. – False The sum of two odd numbers and one even number is even. – True The product of three odd numbers is odd. – True If an even number is divided by 2, the quotient is always odd. – False All prime numbers are odd. – False Prime numbers do not have any factors. – False Sum of two prime numbers is always even. – False 2 is the only even prime number. – True All even numbers are composite numbers. – False The product of two even numbers is always even. – True

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.

 17 and 71 = 1 and 7 are same 37 and 73 = 3 and 7 are same 79 and 97 = 7 and 9 are same

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

 Prime numbers less than 20 are – 2, 3, 5, 7, 11, 13, 17, 19 Composite numbers less than 20 are –  4, 6, 8, 9, 10, 12, 14, 15, 16, 18

Ans – 7

#### Express the following as the sum of two odd numbers:

 44 = 43 + 1 = 44 , 41 + 3 = 44 ,  21 + 23 = 44 , 19+25 = 44 36 = 35 + 1 = 36 , 33 + 3 = 36 , 29 + 7 = 36 24 = 21 + 3 = 24 , 19 + 5 = 24 , 17 + 7 = 24 18 = 17 + 1 = 18 , 15 + 3 = 18 , 13 + 5 = 18

#### Give three pairs of prime numbers whose difference is 2.

 [Remark: Two prime numbers whose difference is 2 are called twin primes.] 3 and 5 – difference is 2 5 and 7 – difference is 2 11 and 13 – difference is 2

#### Which of the following numbers are prime:

(a) 23 (b) 51 (c) 37 (d) 26

23 and 37 are prime [51 and 26 can be divided by 17 and 13]

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

90, 91, 92, 93, 94, 95, 96 – there is no prime numbers between these numbers.

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

•  21 = 3+7+11
• 31 = 3+11+17
• 53 = 13+17+23
• 61=19+29+13

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

2+3 , 3+7 , 7+13 , 3+17 , 2+13

#### 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 neither _______________ nor _______________.

(d) The smallest prime number is _______________.

(e) The smallest composite number is _______________.