Show that `12^n` cannot end with the digits `0` or `5` for any natural number `n`

Explanation

To show that \(12^n\) cannot end with the digits \(0\) or \(5\) for any natural number \(n\), we will analyze the prime factorization of \(12\) and the conditions required for a number to end with specific digits.

### Step 1: Prime Factorization of 12
The first step is to find the prime factorization of \(12\):
\[ 12 = 2^2 \times 3^1 \]
This means that \(12\) is composed of the prime factors \(2\) and \(3\).
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