## The question

Triangle numbers are numbers generated by summing the first n integers, i.e., 1 + 2 + 3 + ... + n

The first ten triangle numbers are:

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?

## Solution

This one is trivial if you implement the formula

${\displaystyle \sum _{k=0}^{N}k={\dfrac {N(N+1)}{2}}}$

You also need a method to count divisors up to sqrt(N), and double that number to yield the total number of factors. You could use a prime number sieve here like the Sieve of Eratosthenes, or just implement a for loop to check for factors using the modulus operator. The highest number you'll need to check the divisibility of is about 8 digits, so you perform the factor check for numbers up to around 12,000.