Playing with Numbers Chapter 3: NCERT Solutions for Class 6 

Overview of the exercises of Chapter 3:  Playing with Numbers 

Before proceeding to the NCERT Solutions Playing with Numbers class 6 Chapter 3 have a look at the exercises prescribed in the chapter to know what the chapter is, there are a total of 7 exercises to be solved.

NCERT Solutions of Playing with Numbers Class 6 Chapter 3 – Exercise 3.1

Question 1: Write all the factors of the following numbers:

(a) 24

24 = 1 × 24
24 = 2 × 12
24 = 3 × 8
24 = 4 × 6
Stop here since 4 and 6 have occurred earlier
Hence, the factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24.

(b) 15

15 = 1 × 15
15 = 3 × 5
Stop here since 3 and 5 have occurred earlier
Hence, the factors of 15 are 1, 3, 5, and 15.

(c) 21

21 = 1 × 21
21 = 3 × 7
Stop here since 3 and 7 have occurred earlier
Hence, the factors of 21 are 1, 3, 7, and 21.

(d) 27

27 = 1 × 27
27 = 3 × 9
Stop here since 3 and 9 have occurred earlier
Hence, the factors of 27 are 1, 3, 9, and 27.

(e) 12

12 = 1 × 12
12 = 2 × 6
12 = 3 × 4
Stop here since 3 and 4 have occurred earlier
Hence, the factors of 12 are 1, 2, 3, 4, 6, and 12.

(f) 20

20 = 1 × 20
20 = 2 × 10
20 = 4 × 5
Stop here since 4 and 5 have occurred earlier
Hence, the factors of 20 are 1, 2, 4, 5, 10, and 20.

(g) 18

18 = 1 × 18
18 = 2 × 9
18 = 3 × 6
Stop here since 3 and 6 have occurred earlier
Hence, the factors of 18 are 1, 2, 3, 6, 9, and 18.

(h) 23

23 = 1 × 23
Since 23 is a prime number, it has only two factors, 1 and 23.
Hence, the factors of 23 are 1 and 23.

(i) 36

36 = 1 × 36
36 = 2 × 18
36 = 3 × 12
36 = 4 × 9
36 = 6 × 6
Stop here since both factors (6) are the same
Hence, the factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.

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Question 2: Write the first five multiples of:

(a) 5

5 × 1 = 5
5 × 2 = 10
5 × 3 = 15
5 × 4 = 20
5 × 5 = 25
Hence, the first five multiples of 5 are 5, 10, 15, 20, and 25.

(b) 8

8 × 1 = 8
8 × 2 = 16
8 × 3 = 24
8 × 4 = 32
8 × 5 = 40
Hence, the first five multiples of 8 are 8, 16, 24, 32, and 40.

(c) 9

9 × 1 = 9
9 × 2 = 18
9 × 3 = 27
9 × 4 = 36
9 × 5 = 45
Hence, the first five multiples of 9 are 9, 18, 27, 36, and 45.

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

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

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

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
Hence, all the multiples of 9 up to 100 are 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, and 99.

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Question 5: What is the sum of any two:

(a) Odd numbers?

The sum of two odd numbers is always an even number.
Example: 5 + 3 = 8

(b) Even numbers?

The sum of two even numbers is always an even number.
Example: 2 + 8 = 10

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Question 6: State whether the following statements are True or False:

• (a) The sum of three odd numbers is even. False
• (b) The sum of two odd numbers and one even number is even. True
• (c) The product of three odd numbers is odd. True
• (d) If an even number is divided by 2, the quotient is always odd. False
• (e) All prime numbers are odd. False
• (f) Prime numbers do not have any factors. False
• (g) Sum of two prime numbers is always even. False
• (h) 2 is the only even prime number. True
• (i) All even numbers are composite numbers. False
• (j) The product of two even numbers is always even. True

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Question 7: The numbers 13 and 31 are prime numbers. Both these numbers have the same digits, 1 and 3. Find such pairs of prime numbers up to 100.

The pairs of prime numbers up to 100 with the same digits are:
17 and 71
37 and 73
79 and 97

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Question 8: Write down separately the prime and composite numbers less than 20.

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

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Question 9: What is the greatest prime number between 1 and 10?

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

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Question 10: Express the following as the sum of two odd primes.

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

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Question 11: Give three pairs of prime numbers whose difference is 2.

(These pairs are called twin primes.)

• (3, 5)
• (5, 7)
• (11, 13)

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Question 12: Which of the following numbers are prime?

• (a) 23 = Prime
• (b) 51 = Composite
• (c) 37 = Prime
• (d) 26 = Composite

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Question 13: Write seven consecutive composite numbers less than 100 so that there is no prime number between them.

The seven consecutive composite numbers less than 100 are 90, 91, 92, 93, 94, 95, and 96.

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Question 14: Express each of the following numbers as the sum of three odd primes.

• (a) 21 = 3 + 5 + 13
• (b) 31 = 3 + 5 + 23
• (c) 53 = 13 + 17 + 23
• (d) 61 = 7 + 13 + 41

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Question 15: Write five pairs of prime numbers less than 20 whose sum is divisible by 5.

• 2 + 3 = 5
• 2 + 13 = 15
• 3 + 17 = 20
• 7 + 13 = 20
• 11 + 19 = 30

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Question 16: Fill in the blanks:

• (a) A number with only two factors is called a prime number.
• (b) A number with more than two factors is called a composite number.
• (c) 1 is neither prime nor composite.
• (d) The smallest prime number is 2.
• (e) The smallest composite number is 4.
• (f) The smallest even number is 2.

NCERT Solutions of Playing with Numbers Class 6 Chapter 3 – Exercise 3.2

Question 1: What is the sum of any two:

(a) Odd numbers?

The sum of two odd numbers is always an even number.
Example: 5 + 3 = 8

(b) Even numbers?

The sum of two even numbers is always an even number.
Example: 2 + 8 = 10

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Question 2: State whether the following statements are True or False:

• (a) The sum of three odd numbers is even. False
• (b) The sum of two odd numbers and one even number is even. True
• (c) The product of three odd numbers is odd. True
• (d) If an even number is divided by 2, the quotient is always odd. False
• (e) All prime numbers are odd. False
• (f) Prime numbers do not have any factors. False
• (g) The sum of two prime numbers is always even. False
• (h) 2 is the only even prime number. True
• (i) All even numbers are composite numbers. False
• (j) The product of two even numbers is always even. True

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Question 3: The numbers 13 and 31 are prime numbers. Both these numbers have the same digits, 1 and 3. Find such pairs of prime numbers up to 100.

Answer The prime numbers with the same digits up to 100 are:
17 and 71
37 and 73
79 and 97

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

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

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Question 5: What is the greatest prime number between 1 and 10?

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

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Question 6: Express the following as the sum of two odd primes.

Answers

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

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Question 7: Give three pairs of prime numbers whose difference is 2.

(These pairs are called twin primes.)

• (3, 5)
• (5, 7)
• (11, 13)

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Question 8: Which of the following numbers are prime?

• (a) 23 = Prime
• (b) 51 = Composite
• (c) 37 = Prime
• (d) 26 = Composite

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

Answer : The seven consecutive composite numbers less than 100 are 90, 91, 92, 93, 94, 95, and 96.

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

Answers

• (a) 21 = 3 + 5 + 13
• (b) 31 = 3 + 5 + 23
• (c) 53 = 13 + 17 + 23
• (d) 61 = 7 + 13 + 41

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

Answers

• 2 + 3 = 5
• 2 + 13 = 15
• 3 + 17 = 20
• 7 + 13 = 20
• 11 + 19 = 30

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Question 12: Fill in the blanks:

• (a) A number with only two factors is called a prime number.
• (b) A number with more than two factors is called a composite number.
• (c) 1 is neither prime nor composite.
• (d) The smallest prime number is 2.
• (e) The smallest composite number is 4.
• (f) The smallest even number is 2.

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NCERT Solutions of Playing with Numbers Class 6 Chapter 3 – Exercise 3.3

Question 1: Using divisibility tests, determine which of the following numbers are divisible by 2, 3, 4, 5, 6, 8, 9, 10, and 11 (say, yes or no):

Number	Divisible by 2	Divisible by 3	Divisible by 4	Divisible by 5	Divisible by 6	Divisible by 8	Divisible by 9	Divisible by 10	Divisible by 11
572	Yes	No	Yes	No	No	No	No	No	No
726352	Yes	Yes	Yes	No	Yes	Yes	No	No	No
5500	Yes	No	Yes	Yes	No	No	No	Yes	No
6000	Yes	No	Yes	Yes	Yes	Yes	No	Yes	No
12159	No	Yes	No	No	No	No	No	No	No
14560	Yes	No	Yes	No	No	Yes	No	No	No
21084	Yes	Yes	Yes	No	Yes	No	No	No	No
31795072	Yes	Yes	Yes	No	Yes	Yes	Yes	No	No
1700	Yes	No	Yes	Yes	No	No	No	Yes	No
2150	No	No	No	Yes	No	No	No	Yes	No

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Question 2: Using divisibility tests, determine which of the following numbers are divisible by 6:

Answer

• (a) 297144 = Yes
• (b) 1258 = No
• (c) 4335 = No
• (d) 61233 = No
• (e) 901352 = No
• (f) 438750 = Yes
• (g) 1790184 = Yes
• (h) 12583 = No
• (i) 639210 = Yes
• (j) 17852 = No

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Question 3: Using divisibility tests, determine which of the following numbers are divisible by 11:

Answer

• (a) 5445 = Yes
• (b) 10824 = Yes
• (c) 7138965 = No
• (d) 70169308 = Yes
• (e) 10000001 = Yes
• (f) 901153 = Yes

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Question 4: Write the smallest digit and the greatest digit in the blank space of each of the following numbers so that the number formed is divisible by 3:

• (a) __ 6724

The smallest digit is 2 and the greatest digit is 8

• (b) 4765 __ 2

The smallest digit is 0 and the greatest digit is 9

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Question 5: Write a digit in the blank space of each of the following numbers so that the number formed is divisible by 11:

• (a) 92__389 = 8
• (b) 8__9484 = 6

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NCERT Solutions of Playing with Numbers Class 6 Chapter 3 – Exercise 3.4

Question 1: Find the common factors of:

• (a) 20 and 28

Common factors: 1, 2, 4

• (b) 15 and 25

Common factors: 1, 5

• (c) 35 and 50

Common factors: 1, 5

• (d) 56 and 120

Common factors: 1, 2, 4, 8

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Question 2: Find the common factors of:

• (a) 4, 8, and 12

Common factors: 1, 2, 4

• (b) 5, 15, and 25

Common factors: 1, 5

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Question 3: Find the first three common multiples of:

• (a) 6 and 8

Common multiples: 24, 48, 72

• (b) 12 and 18

Common multiples: 36, 72, 108

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Question 4: Write all the numbers less than 100, which are common multiples of 3 and 4.

Answer : Common multiples of 3 and 4 less than 100 are: 12, 24, 36, 48, 60, 72, 84, 96

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Question 5: Which of the following numbers are co-prime?

• (a) 18 and 35 = Yes
• (b) 15 and 37 = Yes
• (c) 30 and 415 = No
• (d) 17 and 68 = No
• (e) 216 and 215 = Yes
• (f) 81 and 16 = Yes

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Question 6: A number is divisible by both 5 and 12. By which other number will that number always be divisible?

Answer: The number will also be divisible by 60.

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Question 7: A number is divisible by 12. By what other numbers will that number be divisible?

Answer: The number will also be divisible by its factors: 1, 2, 3, 4, 6, and 12.

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NCERT Solutions of Playing with Numbers Class 6 Chapter 3 – Exercise 3.5

Question 1: Which of the following statements is true?

• (a) If a number is divisible by 3, it must be divisible by 9. False
• (b) If a number is divisible by 9, it must be divisible by 3. True
• (c) A number is divisible by 18 if it is divisible by both 3 and 6. False
• (d) If a number is divisible by 9 and 10, then it must be divisible by 90. True
• (e) If two numbers are co-primes, at least one of them must be prime. False
• (f) All numbers divisible by 4 must also be divisible by 8. False
• (g) All numbers divisible by 8 must also be divisible by 4. True
• (h) If a number exactly divides two numbers separately, it must exactly divide their sum. True
• (i) If a number exactly divides the sum of two numbers, it must exactly divide the two numbers separately. False

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Question 2: Determine if 25110 is divisible by 45.

(Hint: 5 and 9 are co-prime numbers. Test the divisibility of the number by 5 and 9).

Answer: Yes, 25110 is divisible by 45 because it is divisible by both 5 and 9.

NCERT Solutions of Playing with Numbers Class 6 Chapter 3 – Exercise 3.6

Question 1: Find the HCF of the following numbers:

• (a) 18, 48
• (b) 30, 42
• (c) 18, 60
• (d) 27, 63
• (e) 36, 84
• (f) 34, 102
• (g) 70, 105, 175
• (h) 91, 112, 49
• (i) 18, 54, 81
• (j) 12, 45, 75

Solution

• (a) 18, 48 = 6
• (b) 30, 42 = 6
• (c) 18, 60 = 6
• (d) 27, 63 = 9
• (e) 36, 84 = 12
• (f) 34, 102 = 34
• (g) 70, 105, 175 = 35
• (h) 91, 112, 49 = 7
• (i) 18, 54, 81 = 9
• (j) 12, 45, 75 = 3

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Question 2: What is the HCF of two consecutive:

• (a) Numbers?
• (b) Even numbers?
• (c) Odd numbers?

Solution

• (a) HCF of two consecutive Numbers = 1
• (b) HCF of two consecutive Even numbers? = 2
• (c) HCF of two consecutive Odd numbers? = 1

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Question 3: Find the LCM of the following numbers:

• (a) 9 and 4
• (b) 12 and 5
• (c) 6 and 5
• (d) 15 and 4

Solution

• (a) 9 and 4 = 36
• (b) 12 and 5 = 60
• (c) 6 and 5 = 30
• (d) 15 and 4 = 60