Divisor 5563

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

The "Beon Test" for Divisibility by 5563

To determine if any number is divisible by 5563, apply the "Beon 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 134 and subtract this from R.
  3. Take that result and cross off its final digit (units). Take this new number and add 1669 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 5563. That is, your original number is divisible by 5563 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 5563-times tables, it should be easy to visually see if Y is divisible by 5563. If the Y is still much larger than 5563, the above process can be repeated until it does reduce to within small multiples of 5563.

Easy!