Divisor 16631

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

The "Doug Test" for Divisibility by 16631

To determine if any number is divisible by 16631, apply the "Doug 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 214 and add to R.
  3. Take that result and cross off its final digit (units). Take this new number and subtract 1663 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 16631. That is, your original number is divisible by 16631 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 16631-times tables, it should be easy to visually see if Y is divisible by 16631. If the Y is still much larger than 16631, the above process can be repeated until it does reduce to within small multiples of 16631.

Easy!