Divisor 8093

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

The "Andy Crane Test" for Divisibility by 8093

To determine if any number is divisible by 8093, apply the "Andy Crane Test":

  1. If your number ("X") has 5 digits or more, separate the last (smallest) 4 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 5 digits, L = 0 and therefore R = X.
  2. Multiply L by 1907 and add to R.
  3. Take that result and cross off its final digit (units). Take this new number and add 2428 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 8093. That is, your original number is divisible by 8093 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 8093-times tables, it should be easy to visually see if Y is divisible by 8093. If the Y is still much larger than 8093, the above process can be repeated until it does reduce to within small multiples of 8093.

Easy!