Question: Given two positive numbers N and M, find minimal |c — M| where N mod c = 0

Can we solve this problem in O(log (n)) or faster ?

Here is my approach in O(sqrt(n))

int f(int n, int m)
{
    int r = 1;
    int rt = sqrt(n);
    for (int i = 1; i <= rt; ++i)
    {
        if (n % i == 0)
        {
            int j = n / i;
            r = abs(r - m) < abs(j - m) ? r : j;
            r = abs(r - m) < abs(i - m) ? r : i;
        }
    }
    
    return r;
}

Sorry for my bad English ;-;

If I have wrong something, please tell me. It is better to do that than just downvote me because I and someone will learn many new things <3