sol1.c File Reference

Problem 12 solution More...

#include <math.h>
#include <stdio.h>
#include <stdlib.h>

Include dependency graph for sol1.c:

Functions
long	count_divisors (long long n)
	Get number of divisors of a given number. More...
int	main (int argc, char **argv)
	Main function.

Detailed Description

Problem 12 solution

Author

Krishna Vedala

Function Documentation

count_divisors()

long count_divisors

(

long long

n

)

Get number of divisors of a given number.

If \(x = a \times b\), then both \(a\) and \(b\) are divisors of \(x\). Since multiplication is commutative, we only need to search till a maximum of \(a=b = a^2\) i.e., till \(\sqrt{x}\). At every integer till then, there are eaxctly 2 divisors and at \(a=b\), there is only one divisor.

{
    long num_divisors = 0;
 
    for (long long i = 1; i < sqrtl(n) + 1; i++)
        if (n % i == 0)
            num_divisors += 2;
        else if (i * i == n)
            num_divisors += 1;
 
    return num_divisors;
}