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

# --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!).

# --hints--

`euler418()` should return 1177163565297340400.

```js
assert.strictEqual(euler418(), 1177163565297340400);
```

# --seed--

## --seed-contents--

```js
function euler418() {

  return true;
}

euler418();
```

# --solutions--

```js
// solution required
```