Question

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

Answer 1

if the number 6ⁿ ends with the digital 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 factorisation of 6ⁿ is 2 and 3 the uniqueness of the fundamental theorem of arithematic guarantees that these are no other prime in the factorization of 6ⁿ.

Hence it is very clear that thereis novalue of n in natural numbers for which 6ⁿ ends with the digit zero.