Question

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

Answer 1

If any number ends with the digit $0$, it should be divisible by $10$ or in other words, it will also be divisible by $2$ and $5$ as $10 = 2 × 5$
Prime factorisation of $6^n = (2 × 3)^n$
It can be observed that $5$ is not in the prime factorisation of $6 n$ .
Hence, for any value of $n$ , $6 n$ will not be divisible by $5$

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