# 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

**Approach:**

- Number of trailing zeroes would be the highest power of
**16**in the factorial of**N**in**base 10**. - We know that
**16 = 2**. So, the highest power of^{4}**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 <bits/stdc++.h> ` `#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); ` `} ` |

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## 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. ` |

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## 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 ` |

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## 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 ` |

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## PHP

`<?php ` `// PHP implementation of the approach ` ` ` `// Function to return the count of ` `// trailing zeroes ` `function` `getTrailingZeroes(` `$n` `) ` `{ ` ` ` `$count` `= 0; ` ` ` `$val` `; ` `$powerTwo` `= 2; ` ` ` ` ` `// Implementation of the Legendre's formula ` ` ` `do` ` ` `{ ` ` ` `$val` `= (int)(` `$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 ` `$n` `= 6; ` `echo` `(getTrailingZeroes(` `$n` `)); ` ` ` `// This code is contributed by ` `// Code_Mech. ` ` ` `?> ` |

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**Output:**

1

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