---
id: 5900f3861000cf542c50fe99
title: 'Problem 26: Reciprocal cycles'
challengeType: 5
forumTopicId: 301908
dashedName: problem-26-reciprocal-cycles
---
# --description--
A unit fraction contains 1 in the numerator. The decimal representation of the unit fractions with denominators 2 to 10 are given:
1/2 = 0.5
1/3 = 0.(3)
1/4 = 0.25
1/5 = 0.2
1/6 = 0.1(6)
1/7 = 0.(142857)
1/8 = 0.125
1/9 = 0.(1)
1/10 = 0.1
Where 0.1(6) means 0.166666..., and has a 1-digit recurring cycle. It can be seen that 1/7 has a 6-digit recurring cycle.
Find the value of `d` < `n` for which 1/d contains the longest recurring cycle in its decimal fraction part.
# --hints--
`reciprocalCycles(700)` should return a number.
```js
assert(typeof reciprocalCycles(700) === 'number');
```
`reciprocalCycles(700)` should return 659.
```js
assert(reciprocalCycles(700) == 659);
```
`reciprocalCycles(800)` should return 743.
```js
assert(reciprocalCycles(800) == 743);
```
`reciprocalCycles(900)` should return 887.
```js
assert(reciprocalCycles(900) == 887);
```
`reciprocalCycles(1000)` should return 983.
```js
assert(reciprocalCycles(1000) == 983);
```
# --seed--
## --seed-contents--
```js
function reciprocalCycles(n) {
return n;
}
reciprocalCycles(1000);
```
# --solutions--
```js
// solution required
```