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1. NCERT Solutions - Mathematics, Class 6

CHAPTERS

1. Knowing Our Numbers

2. Whole Numbers

3. Playing With Numbers

4. Basic Geometrical Ideas

5. Understanding Elementary Shapes

6. Integers

7. Fractions

8. Decimals

9. Data Handling

10. Mensuration

11. Algebra

12. Ratio and Proportion

13. Symmetry

EXERCISES

1. Exercise 3.1

2. Exercise 3.2

3. Exercise 3.3

4. Exercise 3.4

5. Exercise 3.5

6. Exercise 3.6

7. Exercise 3.7

Q7) The product of three consecutive numbers is always divisible by 6. Verify this statement

with the help of some examples.

Q12) I am the smallest number, having four different prime factors. Can you find me?

Q3) HCF of co-prime numbers 4 and 15 was found as follows by factorisation :

4 = 2 × 2 and 15 = 3 × 5 since there is no common prime factor, so HCF of 4 and 15

is 0. Is the answer correct? If not, what is the correct HCF?

Q1. Which of the following statements are true?

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

(b) If a number is divisible by 9, it must be divisible by 3.

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

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

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

(f) All numbers which are divisible by 4 must also be divisible by 8.

(g) All numbers which are divisible by 8 must also be divisible by 4.

(h) If a number exactly divides two numbers separately, it must exactly divide their

sum.

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

numbers separately.

Q3) Which factors are not included in the prime factorisation of a composite number?

Q8) The sum of two consecutive odd numbers is divisible by 4. Verify this statement with

the help of some examples.

Q4) Write the greatest 4-digit number and express it in terms of its prime factors.

Q9) In which of the following expressions, prime factorisation has been done?

(a) 24 = 2 × 3 × 4 (b) 56 = 7 × 2 × 2 × 2

(c) 70 = 2 × 5 × 7 (d) 54 = 2 × 3 × 9

Q10) Determine if 25110 is divisible by 45.

Q11) 18 is divisible by both 2 and 3. It is also divisible by 2 × 3 = 6. Similarly, a number

is divisible by both 4 and 6. Can we say that the number must also be divisible by

4 × 6 = 24? If not, give an example to justify your answer.

Q5. Write the smallest 5-digit number and express it in the form of its prime factors.

Q6) Find all the prime factors of 1729 and arrange them in ascending order. Now state the

relation, if any; between two consecutive prime factors.

Q2) Here are two different factor trees for 60. Write the missing numbers.

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Mathematics

NCERT Solutions - Mathematics, Class 6

Knowing Our Numbers

Whole Numbers

Playing With Numbers

Basic Geometrical Ideas

Understanding Elementary Shapes

Integers

Fractions

Decimals

Data Handling

Mensuration

Algebra

Ratio and Proportion

Symmetry

Exercise 3.1

Exercise 3.2

Exercise 3.3

Exercise 3.4

Exercise 3.5

Exercise 3.6

Exercise 3.7

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