Is there exist any known method to find divisibility rule of each and every rational number in any numeral system by analysing its reciprocal. And additionally it will give the remainder on division if not divisible.
What I mean to say is I find it out and want to know that its already known or not?
Like if we want to calculate remainder if $2,183,732,179$ is divided by $37$. First we need to find out the reciprocal of $37$ which is $0.027027027.......$. Now count the number of digits in repeating part which is $3$ digits $027$. Now break the digits of dividend in group of three digits each and add all of them.
do it again
Now divide divide $97$ by $37$ we will get same remainder which is $23$.
This is just a simple example, Method is not limited to integers or decimal system.
What I need to know is that method already known or not. If not I need the suggestion which maths/computaional journal may publish the theorem.