Check if count of divisors is even or odd - GeeksforGeeks


Check if count of divisors is even or odd - GeeksforGeeks
Given a number "n", find its total number of divisors are even or odd.

We can observe that the number of divisors is odd only in case of perfect squares. Hence the best solution would be to check if the given number is perfect square or not. If it’s a perfect square, then the number of divisors would be odd, else it’d be even.
void countDivisors(int n)
{
    int root_n = sqrt(n);
 
    // If n is a perfect square, then
    // it has odd divisors
    if (root_n*root_n == n)
        printf("Odd\n");
    else
        printf("Even\n");
}

naive approach would be to find all the divisors and then see if the total number of divisors is even or odd.


Time complexity for such a solution would be O(sqrt(n))
void countDivisors(int n)
{
    // Initialize count of divisors
    int count = 0;
 
    // Note that this loop runs till square root
    for (int i=1; i<=sqrt(n)+1; i++)
    {
        if (n%i==0)
 
            // If divisors are equal,increment
            // count by one
            // Otherwise increment count by 2
            count += (n/i == i)? 1 : 2;
    }
 
    if (count%2==0)
        printf("Even\n");
    else
        printf("Odd\n");
}
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