Divisor 9871

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

The "Georgios Papoutsis Test" for Divisibility by 9871

To determine if any number is divisible by 9871, apply the "Georgios Papoutsis 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 129 and add to R.
  3. Take that result and cross off its final digit (units). Take this new number and subtract 987 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 9871. That is, your original number is divisible by 9871 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 9871-times tables, it should be easy to visually see if Y is divisible by 9871. If the Y is still much larger than 9871, the above process can be repeated until it does reduce to within small multiples of 9871.

Easy!