Question

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

Answer 1

TO CHECK: Whether $6^n$ can end with the digit 0 for any natural number $n$.

We know that,

$6^n=(2\times 3{)}^n$

$6^n=2^n\times 3^n$

Therefore, prime factorization of $6^n$ does not contain $5$ and $2$ as a factor together.

Hence, $6^n$ can never end with the digit 0 for any natural number $n$