# 172. Factorial Trailing Zeroes

Given an integer n, return the number of trailing zeroes in n!.

**Example 1:**

```
Input: 3
Output: 0
Explanation: 3! = 6, no trailing zero.
```

**Example 2:**

```
Input: 5
Output: 1
Explanation: 5! = 120, one trailing zero.
```

**Note:** Your solution should be in logarithmic time complexity.

{% hint style="info" %}
10 = 2 x 5，而2的倍數數量遠多於5倍數的數量，所以這題要找的就是5倍數的數量，但除了5，25、125等等5的次方也要考慮進來。
{% endhint %}

```cpp
int trailingZeroes(int n) { // time: O(logn); space: O(1)
    int res = 0;
    while (n) {
        res += (n / 5);
        n /= 5;
    }
    return res;
}
```


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