Divisor 2309

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

The "Tom Gidden Test" for Divisibility by 2309

To determine if any number is divisible by 2309, apply the "Tom Gidden 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 192 and subtract this from R.
  3. Take that result and cross off its final digit (units). Take this new number and add 231 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 2309. That is, your original number is divisible by 2309 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 2309-times tables, it should be easy to visually see if Y is divisible by 2309. If the Y is still much larger than 2309, the above process can be repeated until it does reduce to within small multiples of 2309.

Easy!