Divisor 5303

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

The "Giorgio Bettineschi Test" for Divisibility by 5303

To determine if any number is divisible by 5303, apply the "Giorgio Bettineschi 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 606 and subtract this from R.
  3. Take that result and cross off its final digit (units). Take this new number and add 1591 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 5303. That is, your original number is divisible by 5303 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 5303-times tables, it should be easy to visually see if Y is divisible by 5303. If the Y is still much larger than 5303, the above process can be repeated until it does reduce to within small multiples of 5303.

Easy!