Divisor 17393

Prime Number:
Yes!
Divisibility test:
The "Balázs Jókay Test"
Test Discovered by:
Matt Parker
Date:
11/11/2024

The "Balázs Jókay Test" for Divisibility by 17393

To determine if any number is divisible by 17393, apply the "Balázs Jókay Test":

  1. If your number ("X") has 8 digits or more, separate the last (smallest) 7 digits from the rest. This makes two smaller numbers, call them Left and Right (note: don't add in trailing zeros to L). If there are fewer than 8 digits, L = 0 and therefore R = X.
  2. Multiply L by 975 and subtract this from R.
  3. Take that result and cross off its final digit (units). Take this new number and add 5218 times the digit you just crossed off. Call this final result "Y".
  4. Y will be much smaller than X, but we have preserved divisibility by 17393. That is, your original number is divisible by 17393 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 17393-times tables, it should be easy to visually see if Y is divisible by 17393. If the Y is still much larger than 17393, the above process can be repeated until it does reduce to within small multiples of 17393.

Easy!