Divisor 4567

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

The "Glenn Sugden Test" for Divisibility by 4567

To determine if any number is divisible by 4567, apply the "Glenn Sugden 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 173 and subtract this from R.
  3. Take that result and cross off its final digit (units). Take this new number and subtract 1370 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 4567. That is, your original number is divisible by 4567 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 4567-times tables, it should be easy to visually see if Y is divisible by 4567. If the Y is still much larger than 4567, the above process can be repeated until it does reduce to within small multiples of 4567.

Easy!