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Check whether $6^n$ can end with the digit 0 for any natural number n.
To do: Here we have to check whether $6^n$ can end with the digit 0 for any natural number $n$.
There is no natural number $n$ for which $6^n$ ends with the digit zero.
If $6^n$ is to end with zero for a natural number $n$, it should be divisible by 2 and 5.
This means that the prime factorisation of $6^n$ should contain the prime number 5 and 2.
But it is not possible because;
$6^n\ =\ (2\ \times\ 3)^n\ =\ 2^n\ \times\ 3^n$
Since 5 is not present in the prime factorization, there is no natural number $n$ for which $6^n$ ends with the digit zero.
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