##
**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?

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**Solution:**

76576500

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**Code:**

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

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; } }

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