### Highly divisible triangular number

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?

Solution:

```void Solution()
{
int i = 1;
int triangleNumber = 0;
do
{
triangleNumber = i * (i + 1) / 2;
i++;
}
while (NoOfDivisors(triangleNumber) <= 500);

Console.WriteLine(triangleNumber);
}

static int NoOfDivisors(int num)
{
//Based on the formula, otherwise it will take infinite time
//Let d(n) be the number of divisors for the natural number, n.
//We begin by writing the number as a product of prime factors: n = paqbrc...
//then the number of divisors, d(n) = (a+1)(b+1)(c+1)...

int counter = 0;
int totalCount = 1;
bool flag = false;
int tempNum = num;
for (int i = 2; i <= num / 2; i++)
{
if (tempNum % i == 0)
{
counter++;
tempNum = tempNum / i;
i--;
flag = true;
continue;

}
if (flag)
{
totalCount = totalCount * (counter + 1);
counter = 0;
flag = false;
}
if (tempNum == 1)
break;
}

return totalCount;
}
```