Divisor 7523

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

The "Seth Arnold Test" for Divisibility by 7523

To determine if any number is divisible by 7523, apply the "Seth Arnold Test":

  1. If your number ("X") has 7 digits or more, separate the last (smallest) 6 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 7 digits, L = 0 and therefore R = X.
  2. Multiply L by 559 and subtract this from R.
  3. Take that result and cross off its final digit (units). Take this new number and add 2257 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 7523. That is, your original number is divisible by 7523 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 7523-times tables, it should be easy to visually see if Y is divisible by 7523. If the Y is still much larger than 7523, the above process can be repeated until it does reduce to within small multiples of 7523.

Easy!