Divisor 10891

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

The "Roberto Selbach Test" for Divisibility by 10891

To determine if any number is divisible by 10891, apply the "Roberto Selbach 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 729 and subtract this from R.
  3. Take that result and cross off its final digit (units). Take this new number and subtract 1089 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 10891. That is, your original number is divisible by 10891 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 10891-times tables, it should be easy to visually see if Y is divisible by 10891. If the Y is still much larger than 10891, the above process can be repeated until it does reduce to within small multiples of 10891.

Easy!