<p>Given an integer <code>n</code>, return <em>the number of trailing zeroes in </em><code>n!</code>.</p>

<p>Note that <code>n! = n * (n - 1) * (n - 2) * ... * 3 * 2 * 1</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> n = 3
<strong>Output:</strong> 0
<strong>Explanation:</strong> 3! = 6, no trailing zero.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> n = 5
<strong>Output:</strong> 1
<strong>Explanation:</strong> 5! = 120, one trailing zero.
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> n = 0
<strong>Output:</strong> 0
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>0 &lt;= n &lt;= 10<sup>4</sup></code></li>
</ul>

<p>&nbsp;</p>
<p><strong>Follow up:</strong> Could you write a solution that works in logarithmic time complexity?</p>

class Solution {
public:
    int trailingZeroes(int n) 
    {
        int count = 0;

        for (int i = 5; i <= n; i += 5)
        {
            int current_factor = i;

            while (current_factor % 5 == 0)
            {
                count++;
                current_factor /= 5;
            }
        }

        return count;
    }
};
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