Divisor 8011

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

The "Jeremy Fitzhardinge Test" for Divisibility by 8011

To determine if any number is divisible by 8011, apply the "Jeremy Fitzhardinge 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 1313 and subtract this from R.
  3. Take that result and cross off its final digit (units). Take this new number and subtract 801 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 8011. That is, your original number is divisible by 8011 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 8011-times tables, it should be easy to visually see if Y is divisible by 8011. If the Y is still much larger than 8011, the above process can be repeated until it does reduce to within small multiples of 8011.

Easy!