Factorial function does not work with large numbers

I am trying to code a function that calculates the factorial of a given number which I defined as follows:

unsigned long long int fact(unsigned long long int n){
    return (n == 0 || n == 1) ? 1 : fact(n - 1) * n;
}

and my main function is:

int main(int argc, const char * argv[]) {
    unsigned long long int z;
    cout << "Please eneter the number: ";
    cin >> z;
    z = fact(z);
    cout << z << endl;
    return 0;
}

The code works fine until 20 but after that garbage value is returned.

I know I can solve the problem using an array but I don't understand why the program runs in such a behavior?