Real Numbers Exercise 1.2
NCERT solutions for Class 10 Maths Real Numbers
NCERT Solutions for Class 10 Maths Real Numbers
1. Express each number as product of its prime factors:
(i) 140
(ii) 156
(iii) 3825
(iv) 5005
(v) 7429
Ans. (i) 140 = 
(ii) 156 = 
= 
(iii) 3825 = 
= 
(iv) 5005 = 
(v) 7429 = 
2. Find the LCM and HCF of the following pairs of integers and verify that 
product of the two numbers.
(i) 26 and 91
(ii) 510 and 92
(iii) 336 and 54
Ans. (i) 26 and 91
HCF = 13
LCM = 
= 182
Product of two numbers 26 and 91 
= 2366
= 2366
Hence, product of two numbers = 
(ii) 510 and 92
HCF = 2
LCM = 
= 23460
Product of two numbers 510 and 92 = 
= 46920
= 46920
Hence, product of two numbers =
(iii) 336 and 54
336= 
54 = 
HCF = 
LCM = 
= 3024
Product of two numbers 336 and 54 = 
= 18144
= 18144
Hence, product of two numbers =
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
Ans. (i) 12, 15 and 21
HCF = 3
LCM = 
= 420
(ii) 17, 23 and 29
HCF = 1
LCM = 
= 11339
(iii) 8, 9 and 25
HCF = 1
LCM = 
= 1800
NCERT Solutions for Class 10 Maths Exercise 1.2
4. Given that HCF (306, 657) = 9, find LCM (306, 657).
Ans. HCF (306, 657) = 9
We know that, LCM × HCF = Product of two numbers
LCM = 22338
NCERT Solutions for Class 10 Maths Exercise 1.2
5. Check whether 6n can end with the digit 0 for any natural number n.
Ans. If any number ends with the digit 0, it should be divisible by 10.
In other words, it will also be divisible by 2 and 5 as 
Prime factorisation of 
It can be observed that 5 is not in the prime factorisation of
.
Hence, for any value of n, will not be divisible by 5.
Therefore, cannot end with the digit 0 for any natural number n.
NCERT Solutions for Class 10 Maths Exercise 1.2
6. Explain why 
and 
are composite numbers.
Ans. Numbers are of two types – prime and composite.
Prime numbers can be divided by 1 and only itself, whereas composite numbers have factors other than 1 and itself.
It can be observed that
= 
= 
= 
The given expression has 6 and 13 as its factors.
Therefore, it is a composite number.
= 
= 
= 
1009 cannot be factorized further
Therefore, the given expression has 5 and 1009 as its factors.
Hence, it is a composite number.
NCERT Solutions for Class 10 Maths Exercise 1.2
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?
Ans. It can be observed that Ravi takes lesser time than Sonia for completing 1 round of the circular path. As they are going in the same direction, they will meet again at the same time when Ravi will have completed 1 round of that circular path with respect to Sonia. And the total time taken for completing this 1 round of circular path will be the LCM of time taken by Sonia and Ravi for completing 1 round of circular path respectively i.e., LCM of 18 minutes and 12 minutes.
And, 
LCM of 12 and 
= 36
Therefore, Ravi and Sonia will meet together at the starting point after 36 minutes.