__Problem____Statement :Problem12__

*The sequence of triangle numbers is generated by adding the natural numbers. So the 7*

^{th}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?*

__Algorithm:__- We solve the problem on a basic assumption that if one factor of the number is present within root of the number the we need not iterate over all the factors till n/2.
- count can be incremented twice just because of the above reason.
- The value of n = i * (i+1) / 2 is evident for i in the

*Solution:*public class problem12 { public static void main(String args[]) { for (int i = 10;; i++) { int n = i * (i + 1) / 2; int count = 2; for (int k = 2; k * k <= n; k++) { if (n % k == 0) count += 2; } if (count >= 500) { System.out.println(n); break; } } } }

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