Divisor 8599

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

The "deemes Test" for Divisibility by 8599

To determine if any number is divisible by 8599, apply the "deemes Test":

  1. If your number ("X") has 8 digits or more, separate the last (smallest) 7 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 8 digits, L = 0 and therefore R = X.
  2. Multiply L by 637 and subtract this from R.
  3. Take that result and cross off its final digit (units). Take this new number and add 860 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 8599. That is, your original number is divisible by 8599 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 8599-times tables, it should be easy to visually see if Y is divisible by 8599. If the Y is still much larger than 8599, the above process can be repeated until it does reduce to within small multiples of 8599.

Easy!