Question

Check whether 6ⁿ can end with the digit 0 for any natural numbers n.

Answer 1

If any number ends with the digit 0, it should be divisible by 10 or in other words its prime factorization must include primes 2 and 5 both as 10 = 2 ×5

Prime factorization of 6ⁿ = (2 ×3)ⁿ

In the above equation it is observed that 5 is not in the prime factorization of 6ⁿ

By Fundamental Theorem of Arithmetic Prime factorization of a number is unique.

So 5 is not a prime factor of 6ⁿ.

Hence, for any value of n, 6ⁿ will not be divisible by 5.

Therefore, 6ⁿ cannot end with the digit 0 for any natural number n.