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:

\[ 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ... \]

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

\[ \begin{align} 1&: 1\\ 3&: 1,3\\ 6&: 1,2,3,6\\ 10&: 1,2,5,10\\ 15&: 1,3,5,15\\ 21&: 1,3,7,21\\ 28&: 1,2,4,7,14,28\end{align} \]

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?