Divisor 8969

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

The "Andrew Holaway Test" for Divisibility by 8969

To determine if any number is divisible by 8969, apply the "Andrew Holaway Test":

  1. If your number ("X") has 8 digits or more, separate the last (smallest) 7 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 8 digits, L = 0 and therefore R = X.
  2. Multiply L by 435 and subtract this from R.
  3. Take that result and cross off its final digit (units). Take this new number and add 897 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 8969. That is, your original number is divisible by 8969 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 8969-times tables, it should be easy to visually see if Y is divisible by 8969. If the Y is still much larger than 8969, the above process can be repeated until it does reduce to within small multiples of 8969.

Easy!