Divisor 7823

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

The "Dávid Borbély Test" for Divisibility by 7823

To determine if any number is divisible by 7823, apply the "Dávid Borbély Test":

  1. If your number ("X") has 7 digits or more, separate the last (smallest) 6 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 7 digits, L = 0 and therefore R = X.
  2. Multiply L by 1344 and subtract this from R.
  3. Take that result and cross off its final digit (units). Take this new number and add 2347 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 7823. That is, your original number is divisible by 7823 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 7823-times tables, it should be easy to visually see if Y is divisible by 7823. If the Y is still much larger than 7823, the above process can be repeated until it does reduce to within small multiples of 7823.

Easy!