highly_divisible_triangular_number

Highly Divisible Triangular Number

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:

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

$$\begin{align} \mathbf 1 &\colon 1\\ \mathbf 3 &\colon 1,3\\ \mathbf 6 &\colon 1,2,3,6\\ \mathbf{10} &\colon 1,2,5,10\\ \mathbf{15} &\colon 1,3,5,15\\ \mathbf{21} &\colon 1,3,7,21\\ \mathbf{28} &\colon 1,2,4,7,14,28 \end{align}$$

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?