Divisor 17683

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

The "Tommy Räjert Test" for Divisibility by 17683

To determine if any number is divisible by 17683, apply the "Tommy Räjert Test":

  1. If your number ("X") has 11 digits or more, separate the last (smallest) 10 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 11 digits, L = 0 and therefore R = X.
  2. Multiply L by 1745 and subtract this from R.
  3. Take that result and cross off its final digit (units). Take this new number and add 5305 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 17683. That is, your original number is divisible by 17683 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 17683-times tables, it should be easy to visually see if Y is divisible by 17683. If the Y is still much larger than 17683, the above process can be repeated until it does reduce to within small multiples of 17683.

Easy!