## Problem:

The sequence of triangle numbers is generated by adding the natural numbers. So the 7th triangle number would be 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28. The first ten terms would be:

1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ...

Let us list the factors of the first seven triangle numbers:

1: 1
3: 1,3
6: 1,2,3,6
10: 1,2,5,10
15: 1,3,5,15
21: 1,3,7,21
28: 1,2,4,7,14,28

We can see that 28 is the first triangle number to have over five divisors.

What is the value of the first triangle number to have over five hundred divisors?

76576500

## Code:The solution may include methods that will be found here: Library.java .

public interface EulerSolution{

public String run();

}
/*
* Solution to Project Euler problem 12
* By Nayuki Minase
*
* http://nayuki.eigenstate.org/page/project-euler-solutions
* https://github.com/nayuki/Project-Euler-solutions
*/

public final class p012 implements EulerSolution {

public static void main(String[] args) {
System.out.println(new p012().run());
}

public String run() {
int num = 0;
for (int i = 1; ; i++) {
num += i;  // num is triangle number i
if (countDivisors(num) > 500)
return Integer.toString(num);
}
}

private static int countDivisors(int n) {
int count = 0;
int end = Library.sqrt(n);
for (int i = 1; i < end; i++) {
if (n % i == 0)
count += 2;
}
if (end * end == n)  // Perfect square
count++;
return count;
}

}