Important Questions for CBSE Class 6 Maths Chapter 3 – Playing with Numbers

Maths is one of the  important subjects taught in school. We require Maths in our daily life to develop the power of analytical skills, reasoning and we begin with mathematical abilities to deal   with numbers in lower classes.

Chapter 3 of Class 6 Maths is about playing with numbers. It includes prime and composite numbers, divisibility, factors and multiples. It also includes two vital concepts- Highest Common Factor (HCF) and Lowest Common Multiple (LCM). The chapter is quite lengthy  and has different questions, and students must practise questions from this chapter to clear their concepts.

Extramarks is a leading educational company that helps students by providing different study materials.  Extramarks subject experts identify the importance of practising questions regularly. For this purpose, they have prepared  the Important Questions Class 6 Maths Chapter 3. They have collected several important questions and provided the solutions in the question series. You may follow this article to solve different types of questions.

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Playing with Numbers Class 6 Extra Questions With Answers

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Question 1. Write down all the factors of the following numbers given below:

(i) 24

(ii)15

(iii)21

(iv)27

(v)12

(vi) 20

(vii) 18

(viii) 23

(ix) 36

Answer 1

(i) 24

24 = 1 × 24

24=2 × 12

24 = 3 × 8

24 = 4 × 6

24 = 6 × 4

Stop here as factors of  4 and 6  have already been counted. .

Therefore, the factors of 24 are – 1,2,3,4,6,8,12 and 24

(ii) 15

15 = 1 × 15

15 = 3 × 5

15 = 5 × 3

Stop here, as factors of  3 and 5 have already been counted.

Therefore, the factors of 15 are – 1, 3, 5 and 15

(iii) 21

21 = 1 × 21

21 = 3 × 7

21 = 7 × 3

Stop here, as factors 3 and 7 have occurred earlier.

Therefore, the factors of 21 are – 1, 3, 7 and 21

(iv) 27

27 = 1 × 27

27 = 3 × 9

27 = 9 × 3

Stop here, as 3 and 9 have occurred earlier.

Therefore, the factors of 27 are – 1, 3, 9 and 27

(v) 12

12 = 1 × 12

12 = 2 × 6

12 = 3 × 4

12 = 4 × 3

Stop here, as the factors of 3 and 4 have already occurred earlier.

Therefore, the factors of 12 are – 1, 2, 3, 4, 6 and 12

(vi) 20

20 = 1 × 20

20 = 2 × 10

20 = 4 × 5

20 = 5 × 4

Stop here as the factors of 4 and 5 have occurred earlier.

Therefore, the factors of 20 are – 1, 2, 4, 5, 10 and 20

(vii) 18

18 = 1 × 18

18 = 2 × 9

18 = 3 × 6

18 = 6 × 3

Stop here, as 3 and 6 have already occurred earlier.

Therefore, the factors of 18 are – 1, 2, 3, 6, 9 and 18

(viii) 23

23 = 1 × 23

23 = 23 × 1

As 1 and 23 have occurred earlier

Therefore, the factors of 23 are – 1 and 23

(ix) 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. Therefore, the factors of 36 are – 1, 2, 3, 4, 6, 9, 12, 18 and 36.

Question 2. Write the first five multiples of:

(i) 5

(ii) 8

(iii) 9

Answer 2

(i) The required five multiples are –

1. 5 × 1 = 5
2. 5 × 2 =10
3. 5 × 3 =15
4. 5 × 4 = 20
5. 5 × 5 = 25

Therefore, the first five multiples of 5 are 5, 10, 15, 20 and 25.

(ii) The required multiples are:

1. 8 × 1 = 8
2. 8 × 2 = 16
3. 8 × 3 = 24
4. 8 × 4 = 32
5. 8 × 5 = 40

Therefore, the first five multiples of 8 are 8, 16, 24, 32 and 40.

(iii) The required multiples are:

1. 9 × 1 = 9
2. 9 × 2 = 18
3. 9 × 3 = 27
4. 9 × 4 = 36
5. 9 × 5 = 45

Therefore, the first five multiples of 9 are 9, 18, 27, 36 and 45.

Question 3. State whether the following statements are True(T) or False(F) –

(i) The total sum of three odd numbers is even.

(ii) The total sum of two odd numbers and one even number is even.

(iii) The product of 3 odd numbers is odd.

(iv) If an even number is divided by two, the quotient is always odd.

(v) All prime numbers are odd.

(vi) Prime numbers don’t have any factors.

(vii) The sum of two prime numbers is always even.

(viii) Two is the only even prime number.

(ix) All the even numbers are composite numbers.

(x) The product of 2 even numbers is always even.

Answer 3

(i) False. The sum of 3 odd numbers is odd.

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

(ii) True. The sum of 2 odd numbers and 1  even number is even.

For example: 3 + 5 + 8 = 16 i.e is an even number.

(iii) True. The product of 3 odd numbers is odd.

For example: 3 × 7 × 9 = 189 i.e is an odd number.

(iv) False. If an even number is divided by two, the quotient is even.

For example: 8 ÷ 2 = 4

(v) False, All the prime numbers are not odd.

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

(vi) False. Since one and the number itself are factors of the number

(vii) False. The sum of 2 prime numbers may also be an odd number

For example: 2 + 5 = 7  which is an odd number.

(viii) True. 2 is the only even and the lowest prime number.

(ix) False. Since 2 is a prime number but not a composite number.

(x) True. The product of 2 even numbers is always even.

For example: 2 × 4 = 8 which is an  even number.

Question 4. The numbers 13 and 31 both are prime numbers. Both of these numbers have the same digits, one and three. Find such pairs of all the prime numbers up to 100.

Answer 4

The prime number pairs with the same digits up to 100 are as follows:

(a) 17 and 71

(b) 37 and 73

(c) 79 and 97

Question 5. Write down separately the prime and composite numbers which are less than 20.

Answer 5:

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

Question 6. What is the greatest prime number between 1 and 10?

Answer 6:

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

Question 7. Express the following given numbers as the sum of two odd primes.

(i) 44

(ii) 36

(iii) 24

(iv) 18

Answer 7

(i) 3 + 41 = 44

(ii) 5 + 31 = 36

(iii) 5 + 19 = 24

(iv) 5 + 13 = 18

Question 8. Which of the following numbers is prime?

(i) 23

(ii) 51

(iii) 37

(iv) 26

Answer 8

(i) 23

1 × 23 = 23

23 × 1 = 23

Therefore, 23 has only 2 factors, that is, 1 and 23. Hence, it is a prime number.

(ii) 51

1 × 51 = 51

3 × 17 = 51

Therefore 51 has 4 factors that are 1, 3, 17 and 51. So, it is not a prime number, and it is a composite number.

(iii) 37

1 × 37 = 37

37 × 1 = 37

Therefore 37 has 2 factors, 1 and 37. Hence, it is a prime number.

(iv) 26

1 × 26 = 26

2 × 13 = 26

Therefore 26 has 4 factors 1, 2, 13 and 26. So, it is not a prime number, and it is a composite number.

Question 9. Express each of the following given numbers as the sum of 3 odd primes:

(i) 21

(ii) 31

(iii) 53

(iv) 61

Answer 9

(i) 3 + 5 + 13 = 21

(ii) 3 + 5 + 23 = 31

(iii) 13 + 17 + 23= 53

(iv) 7 + 13 + 41 = 61

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

Answer 10

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

(i) 2 + 3 = 5

(ii) 2 + 13 = 15

(iii) 3 + 17 = 20

(iv) 7 + 13 = 20

(v) 19 + 11 = 30

Question 11. Fill in the blanks:

(i) A number with only two factors is called a ______.

(ii) A number with more than two factors is called a ______.

(iii) 1 is neither ______ nor ______.

(iv) The smallest prime number is ______.

(v) The smallest composite number is _____.

(vi) The smallest even number is ______.

Answer 11

(i) A number with only two factors is called a prime number.

(ii) A number with more than two factors is called a composite number.

(iii) 1 is neither a prime number nor a composite number.

(iv) The smallest prime number is 2

(v) The smallest composite number is 4

(vi) The smallest even number is 2.

Question 12. By using divisibility tests, determine which of the following given numbers are divisible by 6:

(i) 297144

(ii) 1258

(iii) 4335

(iv) 61233

(v) 901352

(vi) 438750

(vii) 1790184

(viii) 12583

(ix) 639210

(x) 17852

Answer 12

(i) 297144

As the last digit of the number is four. Therefore, the number is divisible by two.

By adding  up all the digits of the number, we get 27 which is divisible by three. Hence, the number is divisible by 3

∴ The number is divisible by both two and three. Hence, the number is divisible by 6

(ii) 1258

As the last digit of the number is eight. Hence, the number is divisible by two.

By adding  up all the digits of the number, we get 16 which is not divisible by three. Hence, the number is not divisible by three.

∴ The number is not divisible by both two and three. Therefore, the number is not divisible by six.

(iii) 4335

Since the last digit of the number is five, which is not divisible by two. Hence, the number is not divisible by two.

By adding all the digits of the number, we get 15 divisible by three. Therefore, the number is divisible by three.

∴ The number is not divisible by two. . Hence, the number is not divisible by six.

(iv) 61233

As the last digit of the number is three, which is not divisible by two. Hence, the number is not divisible by two.

By adding  up all the digits of the number, we get 15 divisible by three. Hence, the number is divisible by three.

∴ The number is not divisible by two.. Hence, the number is not divisible by six.

(v) 901352

As the last digit of the number is two. Hence, the number is divisible by two.

The sum of all the digits of the number, we get 20 which is not divisible by three. Hence, the number is not divisible by three.

∴ The number is not divisible by  three. Hence, the number is not divisible by six.

(vi) 438750

As the last digit of the number is zero. Hence, the number is divisible by two.

By adding  up all the digits of the number, we get 27 which is divisible by three. Hence, the number is divisible by three.

∴ The number is divisible by both two and three. Hence, the number is divisible by six.

(vii) 1790184

As the last digit of the number is four. Hence, the number is divisible by two.

By adding  up all the digits of the number, we get 30 divisible by 3. Hence, the number is divisible by 3

∴ The number is divisible by both two and three. Hence, the number is divisible by 6

(viii) 12583

As the last digit of the number is three. Hence, the number is not divisible by two

By adding  all the digits of the number, we get 19 which is not divisible by three. Hence, the number is not divisible by three.

∴ The number is not divisible by both two and three. Hence, the number is not divisible by six

(ix) 639210

As the last digit of the number is zero. Hence, the number is divisible by two.

By adding  up all the digits of the number, we get 21 which is divisible by three. Hence, the number is divisible by three

∴ The number is divisible by both two and three. Hence, the number is divisible by six.

(x) 17852

As the last digit of the number is two. Hence, the number is divisible by two.

By summing up all the digits of the number, we get 23 which is not divisible by three. Hence, the number is not divisible by three.

∴ The number is not divisible by  three. Hence, the number is not divisible by six.

Question 13. Find the common factors of:

(i) 20 and 28

(ii) 15 and 25

(iii) 35 and 50

(iv) 56 and 120

Answer 13

(i) 20 and 28

1, 2, 4, 5, 10 and 20 are factors of 20

1, 2, 4, 7, 14 and 28 are factors of 28

Common factors = 1, 2, 4

(ii) 15 and 25

1, 3, 5 and 15 are the factors of 15

1, 5 and 25 are the factors of 25

Common factors = 1, 5

(iii) 35 and 50

1,5,7 and 35 are the factors of 35

1, 2, 5, 10, 25 and 50 are the factors of 50

Common factors = 1, 5

(iv) 56 and 120

1,2,4,7,8,14,28 and 56 are the factors of 56

1,2,3,4,5,6,8,10,12,15,20,24,30,40,60 and 120 are factors of 120

Common factors = 1, 2, 4, 8

Question 14. Using divisibility tests, determine which of the following given numbers are divisible by 11:

(i) 5445

(ii) 10824

(iii) 7138965

(iv) 70169308

(v) 10000001

(vi) 901153

Answer 14:

(i) 5445

Sum of digits at odd places = 5 + 4

= 9

Sum of digits at even places = 4 + 5

= 9

Difference between odd place and even place= 9 – 9 = 0

As the difference between the sum of digits at odd places and the sum of digits at even places is zero. Hence, 5445 is divisible by 11

(ii) 10824

Sum of digits at the odd places = 4 + 8 + 1

= 13

Sum of digits at the even places = 2 + 0

= 2

Difference = 13 – 2 = 11

As the difference between the sum of digits at odd places and the sum of digits at even places is 11, which is divisible by 11. Hence, 10824 is divisible by 11

(iii) 7138965

Sum of digits at the odd places = 5 + 9 + 3 + 7 = 24

Sum of digits at the even places = 6 + 8 + 1 = 15

Difference = 24 – 15 = 9

As, the difference between the sum of digits at odd places and the sum of digits at even places is nine, which is not divisible by 11. Hence, 7138965 is not divisible by 11

(iv) 70169308

Sum of digits at the odd places = 8 + 3 + 6 + 0

= 17

Sum of digits at the even places = 0 + 9 + 1 + 7

= 17

Difference = 17 – 17 = 0

As the difference between the sum of digits at odd places and the sum of digits at even places is 0. Hence, 70169308 is divisible by 11

(v) 10000001

Sum of digits at odd places = 1

Sum of digits at even places = 1

Difference = 1 – 1 = 0

As the difference between the sum of digits at odd places and the sum of digits at even places is 0. Hence, 10000001 is divisible by 11

(vi) 901153

Sum of digits at the odd places = 3 + 1 + 0

= 4

Sum of digits at the even places = 5 + 1 + 9

= 15

Difference = 15 – 4 = 11

As, the difference between the sum of digits at odd places and the sum of digits at even places is 11, which is divisible by 11. Hence, 901153 is divisible by 11.

Question 15. Which of the following statements is true?

(i) If the number is divisible by 3, it must be divisible by 9.

(ii) If the number is divisible by 9, it must be divisible by 3.

(iii) A number is divisible by 18 if it is divisible by both 3 and 6.

(iv) If a number is divisible by 9 and 10, then it must be divisible by 90.

(v) If two numbers are co-primes, at least one of them must be prime.

(vi) All numbers divisible by four must also be divisible by 8.

(vii) All numbers divisible by eight must also be divisible by 4.

(viii) If a number exactly divides two numbers separately, it must exactly divide their sum.

(ix) If a number exactly divides the sum of two numbers, it must divide the two numbers separately.

Answer 15

(i) False, six is divisible by three but is not divisible by 9

(ii) True, as 9 = 3 × 3. Therefore, if a number is divisible by nine, it will also be divisible by 3

(iii) False. Since 30 is divisible by both three and six but is not divisible by 18.

(iv) True, as 9 × 10 = 90. Therefore, if the number is divisible by both nine and ten, then it is divisible by 90

(v) False, because 15 and 32 are co-primes and also composite numbers.

(vi) False, as 12 is divisible by four but is not divisible by 8

(vii) True, as 2 × 4 = 8. Therefore, if a number is divisible by eight, it will also be divisible by 2 and 4.

(viii) True, as 2 divides 4 and 8 and it also divides 12 (4 + 8 = 12)

(ix) False, since 2 divides 12, but it does not divide 7 and 5

Benefits of Solving Class 6 Maths Chapter 3 Extra Questions

Extramarks believes in incorporating the best learning experiences through its own repository.To enjoy the maximum benefit of these resources , students just need to register themselves at Extramarks official website and stay ahead of the competition. Practice is a key to getting  better in Maths. Students must solve questions as much as possible to clear their concepts. The experts identify the importance of practice. For this purpose, they have made the Important Questions Class 6 Maths Chapter 3 to help students. They have collected the questions from various sources and provided the answers too. Experienced professionals have further checked the solutions to ensure the best  content for students. Thus, students will have multiple benefits if they follow the Important Questions Class 6 Maths Chapter 3. The benefits are-

• The textbook exercise is often not enough for students. So, they must take help from other references. The experts  have collected questions from different sources so that students need not search for similar study materials for further practice elsewhere. Apart from the textbook, they have taken help from CBSE sample papers and CBSE past years’ question papers. Thus, students  have a complete set of practice study materials at their disposal not just for Maths but for other subjects as well. Students will find one of them in the class 6 playing with numbers extra questions. So, it will help students in revising and practising to get a 100% score in Maths.
• Only solving questions may not be enough to score better in exams. Students must check the answers and get feedback. Sometimes, there can be errors in their processes of solving a problem. Keeping this fact in mind, the experts have also solved the questions and provided detailed solutions with step by step explanation. Experienced professionals have further checked the answers to ensure the answers are foolproof. . Thus, students will find the questions and the solutions in the Important Questions Class 6 Maths Chapter 3.
• The experts have tried to include every kind of question that is usually expected  in exams from the chapter. They have also included questions from past years’ question papers to provide an idea of possible types of questions in exams. Apart from this, they have given the answers in the Chapter 3 Class 6 Maths Important Questions so that students check the answers and solve their doubts. Thus, if students follow the question series, it will increase their confidence, strengthen their knowledge of maths and help them in their  performance.

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