Divisor 16871

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

The "Gordon McDonough Test" for Divisibility by 16871

To determine if any number is divisible by 16871, apply the "Gordon McDonough Test":

  1. If your number ("X") has 6 digits or more, separate the last (smallest) 5 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 6 digits, L = 0 and therefore R = X.
  2. Multiply L by 1226 and subtract this from R.
  3. Take that result and cross off its final digit (units). Take this new number and subtract 1687 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 16871. That is, your original number is divisible by 16871 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 16871-times tables, it should be easy to visually see if Y is divisible by 16871. If the Y is still much larger than 16871, the above process can be repeated until it does reduce to within small multiples of 16871.

Easy!