# C# Program to Count trailing zeroes in factorial of a number

Given an integer n, write a function that returns count of trailing zeroes in n!.  Examples :

```Input: n = 5
Output: 1
Factorial of 5 is 120 which has one trailing 0.

Input: n = 20
Output: 4
Factorial of 20 is 2432902008176640000 which has
4 trailing zeroes.

Input: n = 100
Output: 24```
```Trailing 0s in n! = Count of 5s in prime factors of n!
= floor(n/5) + floor(n/25) + floor(n/125) + ....```

## C#

 `// C# program to count` `// trailing 0s in n!` `using` `System;`   `class` `GFG {`   `    ``// Function to return trailing` `    ``// 0s in factorial of n` `    ``static` `int` `findTrailingZeros(``int` `n)` `    ``{` `        ``// Initialize result` `        ``int` `count = 0;`   `        ``// Keep dividing n by powers` `        ``// of 5 and update count` `        ``for` `(``int` `i = 5; n / i >= 1; i *= 5)` `            ``count += n / i;`   `        ``return` `count;` `    ``}`   `    ``// Driver Code` `    ``public` `static` `void` `Main()` `    ``{` `        ``int` `n = 100;` `        ``Console.WriteLine(``"Count of trailing 0s in "` `                ``+ n + ``"! is "` `+ findTrailingZeros(n));` `    ``}` `}`   `// This code is contributed by vt_m`

Output:

`Count of trailing 0s in 100! is 24`

Time Complexity:  O(log5n)

Auxiliary Space: O(1)

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