Reciprocal cycles


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.






Answer: 
983 
 
Here the logic is to find the remainder of number till it get's repeated.