Divisor 1693

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

The "Matthew Burket Test" for Divisibility by 1693

To determine if any number is divisible by 1693, apply the "Matthew Burket 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 113 and add to R.
  3. Take that result and cross off its final digit (units). Take this new number and add 508 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 1693. That is, your original number is divisible by 1693 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 1693-times tables, it should be easy to visually see if Y is divisible by 1693. If the Y is still much larger than 1693, the above process can be repeated until it does reduce to within small multiples of 1693.

Easy!