Question

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

Answer 1

Any positive integer ending with the digit zero is divisible by 5 and so its prime factorisations must contain the prime 5.

6ⁿ = (2 × 3)ⁿ = 2ⁿ × 3ⁿ

=> The prime in the factorisation of 6ⁿ is 2 and 3.

=> 5 does not occur in the prime factorisation of 6ⁿ for any n.

=> 6ⁿ does not end with the digit zero for any natural number n.

Answer 2

The correct answer is