Divisor 22651

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

The "Adam Berkan Test" for Divisibility by 22651

To determine if any number is divisible by 22651, apply the "Adam Berkan 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 3356 and add to R.
  3. Take that result and cross off its final digit (units). Take this new number and subtract 2265 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 22651. That is, your original number is divisible by 22651 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 22651-times tables, it should be easy to visually see if Y is divisible by 22651. If the Y is still much larger than 22651, the above process can be repeated until it does reduce to within small multiples of 22651.

Easy!