Divisor 20753

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

The "Brandon Frerichs Test" for Divisibility by 20753

To determine if any number is divisible by 20753, apply the "Brandon Frerichs Test":

  1. If your number ("X") has 11 digits or more, separate the last (smallest) 10 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 11 digits, L = 0 and therefore R = X.
  2. Multiply L by 926 and add to R.
  3. Take that result and cross off its final digit (units). Take this new number and add 6226 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 20753. That is, your original number is divisible by 20753 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 20753-times tables, it should be easy to visually see if Y is divisible by 20753. If the Y is still much larger than 20753, the above process can be repeated until it does reduce to within small multiples of 20753.

Easy!