Divisor 8731

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

The "Nathan Bradley Test" for Divisibility by 8731

To determine if any number is divisible by 8731, apply the "Nathan Bradley 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 1269 and add to R.
  3. Take that result and cross off its final digit (units). Take this new number and subtract 873 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 8731. That is, your original number is divisible by 8731 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 8731-times tables, it should be easy to visually see if Y is divisible by 8731. If the Y is still much larger than 8731, the above process can be repeated until it does reduce to within small multiples of 8731.

Easy!