id	title	challengeType	forumTopicId	dashedName
5900f3861000cf542c50fe99	Problem 26: Reciprocal cycles	5	301908	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.

assert(typeof reciprocalCycles(700) === 'number');

reciprocalCycles(700) should return 659.

assert(reciprocalCycles(700) == 659);

reciprocalCycles(800) should return 743.

assert(reciprocalCycles(800) == 743);

reciprocalCycles(900) should return 887.

assert(reciprocalCycles(900) == 887);

reciprocalCycles(1000) should return 983.

assert(reciprocalCycles(1000) == 983);

function reciprocalCycles(n) {

  return n;
}

reciprocalCycles(1000);

// solution required