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

Answers – 

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

4. Find all the multiples of 9 up to 100.

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-

  1. The sum of three odd numbers is even. – False
  2. The sum of two odd numbers and one even number is even. – True
  3. The product of three odd numbers is odd. – True
  4. If an even number is divided by 2, the quotient is always odd. – False
  5. All prime numbers are odd. – False
  6. Prime numbers do not have any factors. – False
  7. Sum of two prime numbers is always even. – False
  8. 2 is the only even prime number. – True
  9. All even numbers are composite numbers. – False
  10. 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

 What is the greatest prime number between 1 and 10?

 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 _______________.

(f) The smallest even number is _______________.

Answers

  1. Prime number
  2. Composite number
  3. Prime number and composite number
  4. 2
  5. 4
  6. 2

 

Chapter 3 Playing with Numbers – Exercise 3.3

  • 128 is divisible by 2,4,8
  • 990 is divisible by 2,3,5,6,9,10,11
  • 1586 is divisible by 2
  • 275 is divisible by 5 , 11
  • 6686 is divisible by 2
  • 639210 is divisible by 2,3,5,6,10,11
  • 429714 is divisible by 2,3,6,9
  • 2856 is divisible by 2,3,4,6,8
  • 3060 is divisible by 2,3,4,5,6,9,10,11
  • 406839 is divisible by 3

Using divisibility test, determine which of the following numbers are divisibly by 4; by 8:
(a) 572 (b) 726352 (c) 5500 (d) 6000 (e) 12159 (f) 14560 (g) 21084 (h) 31795072 (i) 1700 (j) 2150

572 / 4  = Quotient is 143 means divisible by 4 | 572 / 8 = Quotient = 71 ,Remainder =

 

 

 

Chapter 3 Playing with Numbers – Exercise 3.1

 

 

 

 

 

 

 

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Also Read :-

Ncert Solution Class 6 Maths

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