Divisor 4027

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

The "Alyx Test" for Divisibility by 4027

To determine if any number is divisible by 4027, apply the "Alyx 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 675 and subtract this from R.
  3. Take that result and cross off its final digit (units). Take this new number and subtract 1208 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 4027. That is, your original number is divisible by 4027 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 4027-times tables, it should be easy to visually see if Y is divisible by 4027. If the Y is still much larger than 4027, the above process can be repeated until it does reduce to within small multiples of 4027.

Easy!