Chaotic Control

There are some rules to check that a given number is divisible by a number without actual division. e.g. to check if a given number is divisible by 2, you have just check the last digit is even or not. Similarly for 3 , if the sum of digit of any given number is divisible by 3 then the number will also be divisible by 3. One day I was thinking that if there is some generalized rule for every number. Here is some interesting thing I found out. Suppose we have to test divisibility by 17. Let us check whether 4913 is divisible by 17 or not. Here is the rule:- Step 1) :- found out multiple of the number( in this case 17) which ends with 1 or 9. 17 X 3 = 51 ends with 1. Step 2) :- strip the last digit . so we got 5 here. Step 3) :- take the last digit of 4913 which is 3. multiply it by 5 3X5=15. Remove the last digit from 4913 and subtract 15 from it. 491-15 = 476 again repeat this on 476 47 -...