Divisor 21859

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

The "Simon Fox Test" for Divisibility by 21859

To determine if any number is divisible by 21859, apply the "Simon Fox 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 4925 and subtract this from R.
  3. Take that result and cross off its final digit (units). Take this new number and add 2186 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 21859. That is, your original number is divisible by 21859 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 21859-times tables, it should be easy to visually see if Y is divisible by 21859. If the Y is still much larger than 21859, the above process can be repeated until it does reduce to within small multiples of 21859.

Easy!