NCERT Class 10 Solutions: Real Numbers (Chapter 1) Exercise 1.2 –Part 3

Q-4 Given that HCF(306,657)=9 , find LCM(306,657) .


  • Given HCF(306,657)=9

  • By the property that LCM×HCF=Productofthetwonumbers

  • LCM×9=306×657

  • LCM=306×6579

  • LCM=22338

    Therefore LCM(306,657)=22338

Q-5 Check whether 6n can end with the digit 0 for any natural number n.


  • If the number 6n ends with the digit zero, then it is divisible by 5

  • Therefore the prime factorization of 6n contains the prime 5.

  • This is not possible because the only prime in the factorization of 6n is 2 and 3

  • And the uniqueness of the fundamental theorem of arithmetic guarantees that these are no other prime in the factorization of 6n .

    Hence it is very clear that there is no value of n in natural numbers for which 6n ends with the digit zero.

Q-6 Explain why 7×11×13+13 and 7×6×5×4×3×2×1+5 are composite numbers.


Given the prime vs. composite number and find the number are composite or prime

Giventhe Prive vs. Composite Number

Given the prime vs. composite number and find the number are composite or prime

  • Numbers are of two types- prime and composite

  • Prime number can be divided by 1 and only itself.

  • And composite number have factors other than 1 and it self.

    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.

Q-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?


  • Since they both move in the same direction and at the same time

  • To find the time when will they both meet together,

  • It is enough if we find the LCM of 12 and 18

  • 12=22×3×1

  • 18=32×2×1

  • LCM(18,12)=2×3×3×2×1=36

  • Therefore, Sonia and Ravi will meet again after 36 minutes.

Explore Solutions for Mathematics

Sign In