Divisor 6823

Prime Number:
Yes!
Divisibility test:
The "Elisi-Linette Misaki Test"
Test Discovered by:
Matt Parker
Date:
11/11/2024

The "Elisi-Linette Misaki Test" for Divisibility by 6823

To determine if any number is divisible by 6823, apply the "Elisi-Linette Misaki Test":

  1. If your number ("X") has 10 digits or more, separate the last (smallest) 9 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 10 digits, L = 0 and therefore R = X.
  2. Multiply L by 651 and add to R.
  3. Take that result and cross off its final digit (units). Take this new number and add 2047 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 6823. That is, your original number is divisible by 6823 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 6823-times tables, it should be easy to visually see if Y is divisible by 6823. If the Y is still much larger than 6823, the above process can be repeated until it does reduce to within small multiples of 6823.

Easy!