# 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?

``````function getDevisors(num)
{
var list = [];
var large = [];
var n = Math.floor(Math.sqrt(num));

for( var i = 1; i >= n; i++ )
{
if( num % i == 0)
{
list.push(i);

if(i * i != num ){
large.push( num / i );
}
}
}
large.reverse();
return list.concat(large);
}

var triangleNum = 0;
var devisibles = 0;
var cnt = 1;
var result = false;
var logTrack = 100;

while( result == false)
{

triangleNum = triangleNum+cnt;
devisibles = getDevisors(triangleNum);
if(devisibles.length-1> logTrack){
console.log(triangleNum, devisibles.length-1);
logTrack += 100;
}
if( devisibles.length-1 > 500 ){
result = true;
}
cnt++;
}

console.log('result', triangleNum);``````