**Problem 12**

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

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

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

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

**Solution (in Ruby)**

The main aspect about this solution is finding an efficient way to calculate the number of divisors. Lets take a simple example. The number 6 has 4 divisors namely 1,2,3,6. For this number its enough we run upto the Square root of 6 which is integer floored value to be 2. 1 is divisible by 6 by 6 times, so 1 and 6 are divisors. 2 is divisble by 6 3 times, so 2 and 3 are divisors. So totally we have 4 divisors.

There is one more point to be noted here. For a square number such as 16, if we apply this formula, we will end up getting 6 divisors --> 1, 2, 4, 4, 8, 16. You may see we may calculate 4 twice. But it occurs only once for a square number. This special case is handled in the solution given below. The rest is an as-is implementation of the problem statement.

Hover here to see the solution

Cheers!!

Bragaadeesh.

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