NCERT Solutions For Class 6 Maths Exercise 3.5 chapter 3-Playing with Number-pathanto.com

NCERT Solutions For Class 6 Maths Chapter 3

Playing With Numbers

NCERT Solutions For Class 6 Maths chapter 3 Exercise 3.5

Exercise 3.1 Exercise 3.2 Exercise 3.3 Exercise 3.4 Exercise 3.6 Exercise 3.7

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) 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.

Answer 1

(a) False (b) True (c) False (d) True (e) False (f) False (g) True (h) True (i) False

Question 2

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

Answer 2

Question 3

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

Answer 3

1 and the number itself are 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

So,the prime factors of 9999 = 3 x 3 x 11 x 101.

Question 5

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

Answer 5

The smallest 5-digit number = 10000

So,the prime factors: 10000 = 2 x 2 x 2 x 2 x 5 x 5 x 5 x 5.

Question 6

Find all the prime factors of 1729 and arrange them in ascending order. Now state the relations, if any, between the two consecutive prime factors.

Answer 6

the prime factors of 1729 = 7 x 13 x 19. So,the difference between 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

Example 1:
Take three consecutive numbers 3, 4 and 5
4 is divisible by 2
3 is divisible by 3.
So, 3 x 4 x 5 = 60 is divisible by 6.
Example 2:
Take three consecutive numbers 8 ,9 and 10.
8 is divisible by 2.
9 is divisible by 3
8 x 9 x 10 = 720 is divisible by 6.

Question 8

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

Answer 8

Example 1:
two odd number 7 and 9.
7+9 = 16
16 which is divisible by 4.

Example 2:
two odd number 13and 15
13+15=28
28 which 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

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 number.Test the divisibility of the number of 5 and 9.]

Answer 10

prime factorisation of 45 = 5 x 9
Here, 5 and 9 are co-prime numbers.,
unit place of number 25110 is 0. So, it is divisible by 5.
Sum of all digits 9 which is divisible by 9.
So, the given number 25110 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 both 4 and 6. Can we say that the number must also be divisible by 4 x 6 = 24? If not, give an example to justify your answer.