Question:
Check whether 6n can end with the digit 0 for any natural number n.
Solution:
TO CHECK: Whether $6^{n}$ can end with the digit 0 for any natural number $\mathrm{n}$.
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 $n$
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