Divisor 4517

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

The "Damien Conlon Test" for Divisibility by 4517

To determine if any number is divisible by 4517, apply the "Damien Conlon 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 562 and subtract this from R.
  3. Take that result and cross off its final digit (units). Take this new number and subtract 1355 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 4517. That is, your original number is divisible by 4517 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 4517-times tables, it should be easy to visually see if Y is divisible by 4517. If the Y is still much larger than 4517, the above process can be repeated until it does reduce to within small multiples of 4517.

Easy!