Divisor 7537

Prime Number:
Yes!
Divisibility test:
The "Al O'Neill Test"
Test Discovered by:
Matt Parker
Date:
11/11/2024

The "Al O'Neill Test" for Divisibility by 7537

To determine if any number is divisible by 7537, apply the "Al O'Neill Test":

  1. If your number ("X") has 9 digits or more, separate the last (smallest) 8 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 9 digits, L = 0 and therefore R = X.
  2. Multiply L by 916 and subtract this from R.
  3. Take that result and cross off its final digit (units). Take this new number and subtract 2261 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 7537. That is, your original number is divisible by 7537 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 7537-times tables, it should be easy to visually see if Y is divisible by 7537. If the Y is still much larger than 7537, the above process can be repeated until it does reduce to within small multiples of 7537.

Easy!