Project Euler, Problem 12: 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:

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?

I increment up through the triangle numbers until I find one with more than 500 factors.

First I get a triangle number (problem 6), then I find the prime factors (problem 3), then I find the total number of factors by multiplying the exponents of the prime factors together.

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