## Highly divisible triangular number

### Problem 12

Published on Friday, 8th March 2002, 06:00 pm; Solved by 88686

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?