Divisor 25013

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

The "Dr Fill Test" for Divisibility by 25013

To determine if any number is divisible by 25013, apply the "Dr Fill 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 52 and subtract this from R.
  3. Take that result and cross off its final digit (units). Take this new number and add 7504 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 25013. That is, your original number is divisible by 25013 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 25013-times tables, it should be easy to visually see if Y is divisible by 25013. If the Y is still much larger than 25013, the above process can be repeated until it does reduce to within small multiples of 25013.

Easy!