Divisor 13553

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

The "Brett Test" for Divisibility by 13553

To determine if any number is divisible by 13553, apply the "Brett Test":

  1. If your number ("X") has 11 digits or more, separate the last (smallest) 10 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 11 digits, L = 0 and therefore R = X.
  2. Multiply L by 268 and add to R.
  3. Take that result and cross off its final digit (units). Take this new number and add 4066 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 13553. That is, your original number is divisible by 13553 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 13553-times tables, it should be easy to visually see if Y is divisible by 13553. If the Y is still much larger than 13553, the above process can be repeated until it does reduce to within small multiples of 13553.

Easy!