Check whether
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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