Divisor 23567

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

The "Kris Short Test" for Divisibility by 23567

To determine if any number is divisible by 23567, apply the "Kris Short 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 3426 and add to R.
  3. Take that result and cross off its final digit (units). Take this new number and subtract 7070 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 23567. That is, your original number is divisible by 23567 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 23567-times tables, it should be easy to visually see if Y is divisible by 23567. If the Y is still much larger than 23567, the above process can be repeated until it does reduce to within small multiples of 23567.

Easy!