freeCodeCamp/curriculum/challenges/english/08-coding-interview-prep/project-euler/problem-12-highly-divisible-triangular-number.english.md

id	challengeType	title
5900f3781000cf542c50fe8b	5	Problem 12: Highly divisible triangular number

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?

Instructions

Tests

tests:
  - text: <code>divisibleTriangleNumber(5)</code> should return 28.
    testString: assert.strictEqual(divisibleTriangleNumber(5), 28, '<code>divisibleTriangleNumber(5)</code> should return 28.');
  - text: <code>divisibleTriangleNumber(23)</code> should return 630.
    testString: assert.strictEqual(divisibleTriangleNumber(23), 630, '<code>divisibleTriangleNumber(23)</code> should return 630.');
  - text: <code>divisibleTriangleNumber(167)</code> should return 1385280.
    testString: assert.strictEqual(divisibleTriangleNumber(167), 1385280, '<code>divisibleTriangleNumber(167)</code> should return 1385280.');
  - text: <code>divisibleTriangleNumber(374)</code> should return 17907120.
    testString: assert.strictEqual(divisibleTriangleNumber(374), 17907120, '<code>divisibleTriangleNumber(374)</code> should return 17907120.');
  - text: <code>divisibleTriangleNumber(500)</code> should return 76576500.
    testString: assert.strictEqual(divisibleTriangleNumber(500), 76576500, '<code>divisibleTriangleNumber(500)</code> should return 76576500.');

Challenge Seed

function divisibleTriangleNumber(n) {
  // Good luck!
  return true;
}

divisibleTriangleNumber(500);

Solution

function divisibleTriangleNumber(n) {
  let counter = 1;
  let triangleNumber = counter++;

  function getFactors(num) {
    let factors = [];

    let possibleFactor = 1;
    let sqrt = Math.sqrt(num);

    while (possibleFactor <= sqrt) {
      if (num % possibleFactor == 0) {
        factors.push(possibleFactor);
        var otherPossibleFactor = num / possibleFactor;
        if (otherPossibleFactor > possibleFactor) {
          factors.push(otherPossibleFactor);
        }
      }
      possibleFactor++;
    }

    return factors;
  }

  while (getFactors(triangleNumber).length < n) {
    triangleNumber += counter++;
  }
  console.log(triangleNumber)
  return triangleNumber;
}