**Problem 26:**

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* < 1000 for which ^{1}/_{d} contains the longest recurring cycle in its decimal fraction part.

**Idea:**

I had no idea how to easily calculate the length of a recurring cycle, especially for odd, made up cases such as: *0.111567111567…*. How would I know, programmatically, if once I reach “1115” that it is no longer a recurring cycle (of ones), but to keep going to include “67” to complete the cycle?

//Did not implement

While researching Repeating Decimals, I found out these are called cyclic numbers. Upon researching more about cyclic numbers (and how to calculate them), I came across the Wikipedia article that appeared to go up to (but not exceeding) 1000.