# 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++ 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); ` `} ` |

*chevron_right*

*filter_none*

**Output:**

1

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