---
id: 5900f50f1000cf542c510021
challengeType: 5
title: 'Problem 418: Factorisation triples'
forumTopicId: 302087
---

## Description
<section id='description'>
Let n be a positive integer. An integer triple (a, b, c) is called a factorisation triple of n if: 1 ≤ a ≤ b ≤ c
 a·b·c = n.

Define f(n) to be a + b + c for the factorisation triple (a, b, c) of n which minimises c / a. One can show that this triple is unique.


For example, f(165) = 19, f(100100) = 142 and f(20!) = 4034872.


Find f(43!).
</section>

## Instructions
<section id='instructions'>

</section>

## Tests
<section id='tests'>

```yml
tests:
  - text: <code>euler418()</code> should return 1177163565297340400.
    testString: assert.strictEqual(euler418(), 1177163565297340400);

```

</section>

## Challenge Seed
<section id='challengeSeed'>

<div id='js-seed'>

```js
function euler418() {

  return true;
}

euler418();
```

</div>



</section>

## Solution
<section id='solution'>

```js
// solution required
```

</section>