Numarul divizorilor unui numar | Algoritmi eficienti

//Varianta 1:

int numar_divizori(int x)
{
        int c=0,div;

    for (div=1; div * div < x; div++)  // div se duce pana la sqrt x
        if (x % div == 0)
        c+=2;

    if ( div * div == x)  // in cazul in care e patrat perfect
        c++;

    return c;
}

//Varianta 2:

int number_of_divisors(int x)
{
    int limit = x;
    int numberOfDivisors = 0;

    if (x == 1) return 1;

    for (int i = 1; i < limit; ++i)
        if (x % i == 0)
            {
            limit = x / i;
            if (limit != i)
                {
                    numberOfDivisors++;
                }
            numberOfDivisors++;
            }


    return numberOfDivisors;
}