Real Numbers - Prime Factorisation

Ex 1.2 Q5. CBSE 10th Maths NCERT exercise solution.
NCERT Solutions for Class 10 Maths | Chapter: Real Numbers | Concept: Fundamental Theorem of Arithmetic: Prime factorisation of a positive integer is unique

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

Explanatory Answer

6n = (2 × 3)n = 2n × 3n

The only primes in the factorization of 6n are 2 and 3.
The uniqueness of the Fundamental Theorem Of Arithmetic ensures that there are no other prime numbers in the factorization of 6n.
Unless the prime factorization of a number includes 2 and 5, the number will not end in ‘0’.
Because prime factorization of 6n does not include 2 and 5, it will not end in '0'.

∴ There exists no natural numbers ‘n’ for which 6n will end the digit zero.