Divisor 21767

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

The "Dave Bell Test" for Divisibility by 21767

To determine if any number is divisible by 21767, apply the "Dave Bell 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 763 and add to R.
  3. Take that result and cross off its final digit (units). Take this new number and subtract 6530 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 21767. That is, your original number is divisible by 21767 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 21767-times tables, it should be easy to visually see if Y is divisible by 21767. If the Y is still much larger than 21767, the above process can be repeated until it does reduce to within small multiples of 21767.

Easy!