Divisor 8597

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

The "mscha Test" for Divisibility by 8597

To determine if any number is divisible by 8597, apply the "mscha Test":

  1. If your number ("X") has 9 digits or more, separate the last (smallest) 8 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 9 digits, L = 0 and therefore R = X.
  2. Multiply L by 304 and subtract this from R.
  3. Take that result and cross off its final digit (units). Take this new number and subtract 2579 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 8597. That is, your original number is divisible by 8597 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 8597-times tables, it should be easy to visually see if Y is divisible by 8597. If the Y is still much larger than 8597, the above process can be repeated until it does reduce to within small multiples of 8597.

Easy!