Highly-Divisible-Triangular-Number.js

/*
Description: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 n divisors?

Examples:
divisibleTriangleNumber(5) should return 28.
divisibleTriangleNumber(23) should return 630.
divisibleTriangleNumber(167) should return 1385280.
divisibleTriangleNumber(374) should return 17907120.
divisibleTriangleNumber(500) should return 76576500.
*/


//get the factors of the triangle number
function fact(n) {
    let factors = [];
    for (let i = 1; i <= Math.sqrt(n); i++) {
      if (n % i === 0) {
        factors.push(i);
        if (n / i !== i) {
          factors.push(n / i);
        }
      }
    }
    return factors;
  }
  
  function divisibleTriangleNumber(n) {
    let i = 1
    let factors = 0;
    let tri = 0;
    while(factors<=n){
      //compute the next triangle number
      tri = (i*(i+1)) / 2
      //get the length of its divisors
      factors = fact(tri).length
      //then increment i to get the next traingle number 
      //in the next iteration
      i += 1
    }
    return tri
  }
  
  divisibleTriangleNumber(167);