Divisor 1907

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

The "Hau Kai Test" for Divisibility by 1907

To determine if any number is divisible by 1907, apply the "Hau Kai Test":

  1. If your number ("X") has 10 digits or more, separate the last (smallest) 9 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 10 digits, L = 0 and therefore R = X.
  2. Multiply L by 288 and subtract this from R.
  3. Take that result and cross off its final digit (units). Take this new number and subtract 572 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 1907. That is, your original number is divisible by 1907 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 1907-times tables, it should be easy to visually see if Y is divisible by 1907. If the Y is still much larger than 1907, the above process can be repeated until it does reduce to within small multiples of 1907.

Easy!