¡Número de ceros finales en base 16 representación de N!

Dado un número entero N , la tarea es encontrar el número de ceros finales en la representación en base 16 del factorial de N .
Ejemplos: 
 

Entrada: N = 6 
Salida: 1 
6! = 720 (base 10) = 2D0 (base 16)
Entrada: N = 100 
Salida: 24 
 

Acercarse: 
 

• El número de ceros finales sería la potencia más alta de 16 en el factorial de N en base 10 .
• Sabemos que 16 = 2 ⁴ . Entonces, la potencia más alta de 16 es igual a la potencia más alta 2 en el factorial de N dividido por 4 .
• Para calcular la mayor potencia de 2 en N! , podemos usar la fórmula de Legendre .

A continuación se muestra la implementación del enfoque anterior: 
 

// 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);
}

// 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 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# 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
// 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.
 
?>

<script>
 
// JavaScript implementation of the approach
 
// Function to return the count of trailing zeroes
function getTrailingZeroes(n)
{
    let count = 0;
    let val, powerTwo = 2;
 
    // Implementation of the Legendre's formula
    do {
        val = Math.floor(n / powerTwo);
        count += val;
        powerTwo *= 2;
    } while (val != 0);
 
    // Count has the highest power of 2
    // that divides n! in base 10
    return (Math.floor(count / 4));
}
 
// Driver code
 
    let n = 6;
    document.write(getTrailingZeroes(n));
 
 
// This code is contributed by Surbhi Tyagi
 
</script>

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