Question
Check whether $6^n$ can end with the digit $0$ for any natural number $n$.
✓
Answer
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 $10 = 2 \times 5$ 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 $n$.
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 $n$.
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