Divisor 1999

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

The "Stuart Sewell Test" for Divisibility by 1999

To determine if any number is divisible by 1999, apply the "Stuart Sewell 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 5 and add to R.
  3. Take that result and cross off its final digit (units). Take this new number and add 200 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 1999. That is, your original number is divisible by 1999 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 1999-times tables, it should be easy to visually see if Y is divisible by 1999. If the Y is still much larger than 1999, the above process can be repeated until it does reduce to within small multiples of 1999.

Easy!