Question

Check whether 6ⁿ can end with the digit 0? Justify your answer.

Answer 1

If any number ends with the digit 0, it should be divisible by 10. In other words, its prime factorisation must include primes 2 and 5.
Prime factorisation of 6ⁿ = (2 x 3)ⁿ
By the Fundamental Theorem of Arithmetic, prime factorisation of a number is unique.
5 is not a prime factor of 6ⁿ.
Hence, for any value of n, 6n will not be divisible by 5.
Hence, 6ⁿ cannot end with the digit 0 for any natural number n.