CountFactors.php

<?php

/*
A positive integer D is a factor of a positive integer N 
if there exists an integer M such that N = D * M.

For example, 6 is a factor of 24, because M = 4 satisfies the above condition (24 = 6 * 4).

Write a function:

    function solution($N); 

that, given a positive integer N, returns the number of its factors.

For example, given N = 24, the function should return 8, because 24 has 8 factors, 
namely 1, 2, 3, 4, 6, 8, 12, 24. There are no other factors of 24.

Assume that:
        N is an integer within the range [1..2,147,483,647].

Complexity:
        expected worst-case time complexity is O(sqrt(N));
        expected worst-case space complexity is O(1).
*/

/*
 * CODILITY ANALYSIS: https://codility.com/demo/results/demoJN2RAJ-CAC/
 * LEVEL: EASY
 * Correctness:	100%
 * Performance:	100%
 * Task score:	100%
 */
function solution($N)
{
	// number of factors/divisors
	$factorsCount = 0;

	// for example, if N = 36, factors are [1, 2, 3, 4, 6, 9, 12, 18]
	// we use i * i < n formula to count divisors
	$i = 1;
	while($i * $i <= $N)
	{
		if($N % $i == 0)
		{
			// factors are mirrored, so we add +2
			// i = 1, 36 / 1 = 36 exist,
			// i = 2, 36 / 2 = 18 exist,
			// i = 3, 36 / 3 = 12 exist, etc...
			if($i * $i < $N)
				$factorsCount += 2;
			// i = 6, 36 / 6 = 6 exist,
			// we don't want to count same factor twice, so we add +1
			else
				$factorsCount += 1;
		}
		$i++;
	}

	return $factorsCount;
}