• Skip to main content
  • Skip to secondary menu
  • Skip to primary sidebar

Class Notes

Free Class Notes & Study Material

  • Class 1-5
  • Class 6
  • Class 7
  • Class 8
  • Class 9
  • Class 10
  • Class 11
  • Class 12
  • NCERT SOL
  • Ref Books
Home » NCERT Solutions » Class 6 » Maths » Chapter 3 Playing with Numbers » Exercise 3.5

Exercise 3.5

Last Updated on July 3, 2023 By Mrs Shilpi Nagpal

Class 6 Mathematics Chapter 3 |
Playing with Numbers | Exercise 3.5

Question 1: 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) If a number is divisible by 18, it must be 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 by divisible by 8.

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

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

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

Answer 1: Statements (b), (c), (d), (g) and (h) are true.

Question 2: Here are two different factor trees for 60. Write the missing numbers.

Question 2

Answer :

Answer 2

Question 3: Which factors are not included in the prime factorisation of a composite number?

Answer 3: 1 is the factor which is not included in the prime factorisation of a composite number.

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

Answer 4: The greatest 4-digit number = 9999

Question 4

Question 5: Write the smallest 5-digit number and express it in terms of its prime factors. Answer 5: The smallest five digit number is 10000.

Answer 5:

Answer 5

The prime factors of 10000 are 2 × 2 × 2 × 2 × 5 × 5 × 5 × 5.

Question 6: Find all the prime factors of 1729 and arrange them in ascending order. Now state the relation, if any, between, two consecutive prime numbers.

Answer 6: Prime factors of 1729 are 7 × 13 × 19.

Answer 6

The difference of two consecutive prime factors is 6.

Question 7: The product of three consecutive numbers is always divisible by 6. Verify this statement with the help of some examples.

Answer 7:  (i) 2 x 3 x 4 = 24 which is divisible by 6

(ii) 4 x 5 x 6 = 120 which is divisible by 6

(iii) 9 × 10 × 11= 990 which is divisible by 6

Question 8: The sum of two consecutive odd numbers is always divisible by 4. Verify this statement with the help of some examples.

Answer 8: 3 + 5 = 8 and 8 is divisible by 4.

5 + 7 = 12 and 12 is divisible by 4.

7 + 9 = 16 and 16 is divisible by 4.

9 + 11 = 20 and 20 is divisible by 4.

Question 9: In which of the following expressions, prime factorisation has been done:

(a) 24 = 2 x 3 x 4

(b) 56 = 7 x 2 x 2 x 2

(c) 70 = 2 x 5 x 7

(d) 54 = 2 x 3 x 9

Answer 9: In expressions (b) and (c), prime factorisation has been done.

Question 10: 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 10: The prime factorisation of 45 = 5 x 9

Factors of 5 =1,5

Factors of 9 = 1,3,9

25110 is divisible by 5 as ‘0’ is at its unit place.

25110 is divisible by 9 as sum of digits is divisible by 9.

Since the number is divisible both by 5 and 9 both, it is divisible by 45.

Question 11: 18 is divisible by both 2 and 3. It is also divisible by 2 x 3 = 6. Similarly, a number is divisible by 4 and 6. Can we say that the number must be divisible by 4 x 6 = 24? If not, give an example to justify your answer.

Answer 11: No. it is not necessary because 12 and 36 are divisible by 4 and 6 both, but are not divisible by 24.

Question 12: I am the smallest number, having four different prime factors. Can you find me?

Answer 12: The smallest four prime numbers are 2, 3, 5 and 7.

Hence, the required number is 2 x 3 x 5 x 7 = 210

Filed Under: Chapter 3 Playing with Numbers, Class 6, Maths, NCERT Solutions

About Mrs Shilpi Nagpal

Author of this website, Mrs. Shilpi Nagpal is MSc (Hons, Chemistry) and BSc (Hons, Chemistry) from Delhi University, B.Ed. (I. P. University) and has many years of experience in teaching. She has started this educational website with the mindset of spreading free education to everyone.

Reader Interactions

Leave a Reply

Your email address will not be published. Required fields are marked *

Primary Sidebar

  • Facebook
  • Pinterest
  • Twitter
  • YouTube

CATEGORIES

  • —— Class 6 Notes ——
  • —— Class 7 Notes ——
  • —— Class 8 Notes ——
  • —— Class 9 Notes ——
  • —— Class 10 Notes ——
  • —— NCERT Solutions ——

© 2016 - 2025 · Disclaimer · Privacy Policy · About Us · Contact Us