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Prove that, for a natural number $n$, $6^n$ can not end with the digit $0$. Which prime number must be multiplied with $6^n$ so that the resultant ends with the digit zero?
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Solution: $6^n = 2^n \times 3^n$
To end with the digit $0$, $6^n$ should have $2$ and $5$ both as prime factors.
$\therefore 6^n$ cannot end with the digit $0$.
To end with digit $0$, $6^n$ should be multiplied by the prime number $5$.
To end with the digit $0$, $6^n$ should have $2$ and $5$ both as prime factors.
$\therefore 6^n$ cannot end with the digit $0$.
To end with digit $0$, $6^n$ should be multiplied by the prime number $5$.