Divisor 25703

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

The "Simeon Baker Test" for Divisibility by 25703

To determine if any number is divisible by 25703, apply the "Simeon Baker Test":

  1. If your number ("X") has 10 digits or more, separate the last (smallest) 9 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 10 digits, L = 0 and therefore R = X.
  2. Multiply L by 918 and subtract this from R.
  3. Take that result and cross off its final digit (units). Take this new number and add 7711 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 25703. That is, your original number is divisible by 25703 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 25703-times tables, it should be easy to visually see if Y is divisible by 25703. If the Y is still much larger than 25703, the above process can be repeated until it does reduce to within small multiples of 25703.

Easy!