# Number of trailing zeroes in base 16 representation of N!

Given an integer N, the task is to find the number of trailing zeroes in the base 16 representation of the factorial of N.

Examples:

Input: N = 6
Output: 1
6! = 720 (base 10) = 2D0 (base 16)

Input: N = 100
Output: 24

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach:

• Number of trailing zeroes would be the highest power of 16 in the factorial of N in base 10.
• We know that 16 = 24. So, the highest power of 16 is equal to the highest power 2 in the factorial of N divided by 4.
• To calculate the highest power of 2 in N!, we can use Legendre’s Formula.

Below is the implementation of the above approach:

## C++

 `// C++ implementation of the approach ` `#include ` `#define ll long long int ` `using` `namespace` `std; ` ` `  `// Function to return the count of trailing zeroes ` `ll getTrailingZeroes(ll n) ` `{ ` `    ``ll count = 0; ` `    ``ll val, powerTwo = 2; ` ` `  `    ``// Implementation of the Legendre's formula ` `    ``do` `{ ` `        ``val = n / powerTwo; ` `        ``count += val; ` `        ``powerTwo *= 2; ` `    ``} ``while` `(val != 0); ` ` `  `    ``// Count has the highest power of 2 ` `    ``// that divides n! in base 10 ` `    ``return` `(count / 4); ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``int` `n = 6; ` `    ``cout << getTrailingZeroes(n); ` `} `

## Java

 `// Java implementation of the approach  ` `class` `GfG  ` `{ ` ` `  `// Function to return the count of trailing zeroes  ` `static` `long` `getTrailingZeroes(``long` `n)  ` `{  ` `    ``long` `count = ``0``;  ` `    ``long` `val, powerTwo = ``2``;  ` ` `  `    ``// Implementation of the Legendre's formula  ` `    ``do`  `    ``{  ` `        ``val = n / powerTwo;  ` `        ``count += val;  ` `        ``powerTwo *= ``2``;  ` `    ``} ``while` `(val != ``0``);  ` ` `  `    ``// Count has the highest power of 2  ` `    ``// that divides n! in base 10  ` `    ``return` `(count / ``4``);  ` `}  ` ` `  `// Driver code  ` `public` `static` `void` `main(String[] args)  ` `{  ` `    ``int` `n = ``6``;  ` `    ``System.out.println(getTrailingZeroes(n));  ` `}  ` `} ` ` `  `// This code is contributed by  ` `// Prerna Saini. `

## Python3

 `# Python3 implementation of the approach ` ` `  `# Function to return the count of ` `# trailing zeroes ` `def` `getTrailingZeroes(n): ` ` `  `    ``count ``=` `0` `    ``val, powerTwo ``=` `1``, ``2` ` `  `    ``# Implementation of the Legendre's  ` `    ``# formula ` `    ``while` `(val !``=` `0``): ` `        ``val ``=` `n ``/``/``powerTwo ` `        ``count ``+``=` `val ` `        ``powerTwo ``*``=` `2` ` `  `    ``# Count has the highest power of 2 ` `    ``# that divides n! in base 10 ` `    ``return` `(count ``/``/` `4``) ` ` `  `# Driver code ` `n ``=` `6` `print``(getTrailingZeroes(n)) ` ` `  `# This code is contributed  ` `# by Mohit Kumar `

## C#

 `// C# implementation of the approach  ` `using` `System; ` `class` `GFG  ` `{ ` ` `  `// Function to return the count of ` `// trailing zeroes  ` `static` `long` `getTrailingZeroes(``long` `n)  ` `{  ` `    ``long` `count = 0;  ` `    ``long` `val, powerTwo = 2;  ` ` `  `    ``// Implementation of the  ` `    ``// Legendre's formula  ` `    ``do` `    ``{  ` `        ``val = n / powerTwo;  ` `        ``count += val;  ` `        ``powerTwo *= 2;  ` `    ``} ``while` `(val != 0);  ` ` `  `    ``// Count has the highest power of 2  ` `    ``// that divides n! in base 10  ` `    ``return` `(count / 4);  ` `}  ` ` `  `// Driver code  ` `public` `static` `void` `Main()  ` `{  ` `    ``int` `n = 6;  ` `    ``Console.Write(getTrailingZeroes(n));  ` `}  ` `} ` ` `  `// This code is contributed by  ` `// Akanksha Rai `

## PHP

 ` `

Output:

```1
```

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