Рекурсивная функция вычисляющая факториал числа

#include<iostream>
using namespace std;
unsigned long long factorial(int);
unsigned long long sum = 1;
int main()
{
    int number;
    cout<<"Enter the number, the factorial of which you would like to learn: ";
    while (cin >> number && !isalpha(number))
    {
        if (!number)
            cout<<number<<"! = "<<1<<"\nNext number: ";
    
        else
        {
        
            unsigned long long sum = factorial(number);
            cout<<number<<"! = "<<sum;
            cout<<"\nNext number('q' quit): ";
        }
    }
    cout<<"Bye";
    return 0;
}
unsigned long long factorial(int n)
{
    sum *= n;
    if (n > 1)
        factorial(n-1); 
    return sum;
    
}

unsigned long long factorial(int n)
{
      if (n <= 1)
             return 1;
      return n*factorial(n-1); 
}

 // factorial naive implementation
    
 static const BigInt factorial(unsigned long long  n) {
    BigInt fact = 1;
    for (unsigned long long i = 1; i <= n; i++)
        fact *= i;
    return fact;
}