---
id: 5900f3b61000cf542c50fec9
challengeType: 5
title: 'Problem 74: Digit factorial chains'
forumTopicId: 302187
---
## Description
The number 145 is well known for the property that the sum of the factorial of its digits is equal to 145:
1! + 4! + 5! = 1 + 24 + 120 = 145
Perhaps less well known is 169, in that it produces the longest chain of numbers that link back to 169; it turns out that there are only three such loops that exist:
169 → 363601 → 1454 → 169
871 → 45361 → 871
872 → 45362 → 872
It is not difficult to prove that EVERY starting number will eventually get stuck in a loop. For example,
69 → 363600 → 1454 → 169 → 363601 (→ 1454)
78 → 45360 → 871 → 45361 (→ 871)
540 → 145 (→ 145)
Starting with 69 produces a chain of five non-repeating terms, but the longest non-repeating chain with a starting number below one million is sixty terms.
How many chains, with a starting number below one million, contain exactly sixty non-repeating terms?
## Instructions
## Tests
```yml
tests:
- text: digitFactorialChains() should return a number.
testString: assert(typeof digitFactorialChains() === 'number');
- text: digitFactorialChains() should return 402.
testString: assert.strictEqual(digitFactorialChains(), 402);
```
## Challenge Seed
```js
function digitFactorialChains() {
return true;
}
digitFactorialChains();
```
## Solution
```js
// solution required
```