NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers Ex 1.2

Ex 1.2 Class 10 Question 1.
Express each number as a product of its prime factors:
(i) 140
(ii) 156
(iii) 3825
(iv) 5005
(v) 7429.
Solutions:
(i) 140

(ii) 156

(iii) 3825

(iv) 5005

(v) 7429.
So, 7429 = 17 x 19 x 23

Exercise 1.2 Class 10 Maths Question 2.
Find the LCM and HCF of the following pairs of integers and verify that LCM x HCF = product of two numbers,
(i) 26 and 91
(ii) 510 and 92
(iii) 336 and 54
Solutions:
(i) 26 and 91

(ii) 510 and 92

(iii) 336 and 54

1.2 Class 10 Maths Chapter 1 Question 3.
Find the LCM and HCF of the following integers by applying the prime factorisation method.
(i) 12,15 and 21
(ii) 17,23 and 29
(iii) 8, 9 and 25
Solutions:
(i) 12,15 and 21

(ii) 17,23 and 29

(iii) 8, 9 and 25

Exercise 1.2 Class 10 Question 4.
Given that HCF (306,657) = 9, find LCM (306, 657).
Solutions:
Given that HCF (306, 657) = 9
We know that LCM x HCF = Product of two numbers

Class 10 Maths Chapter 1 Exercise 1.2 Question 5.
Check whether 6ⁿ can end with the digit 0 for any natural number n.
Solutions:
Since prime factorisation of 6ⁿ is given by 6ⁿ = (2 x 3)ⁿ = 2ⁿ x 3ⁿ
Prime factorisation of 6ⁿ contains only prime numbers 2 and 3.
6ⁿ may end with the digit 0 for some ‘n’ if 5 must be in its prime factorisation which is not present.
So, there is no natural number VT for which 6ⁿ ends with the digit zero.

Ex 1.2 Class 10 Maths Question 6.
Explain why 7 x 11 x 13 + 13 and 7 x 6 x 5 x 4 x 3 x 2 x 1 + 5 are composite numbers.
Solutions:

Both N₁ and N₂ are expressed as a product of primes. Therefore, both are composite numbers.

Exercise 1.2 Class 10 Maths Question 7.
There is a circular path around a sports field. Sonia takes 18 minutes to drive one round of the field, while Ravi takes 12 minutes for the same. Suppose they both start at the same point and at the same time, and go in the same direction. After how many minutes will they meet again at the starting point?
Solutions:
By taking LCM of time taken (in minutes) by Sonia and Ravi, we can get the actual number of minutes after which they meet again at the starting point after both start at same point and of the same time, and go in the same direction.

Therefore, both Sonia and Ravi will meet again at the starting point after 36 minutes.

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