Divisor 13901

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

The "aNDreas Bolotă Test" for Divisibility by 13901

To determine if any number is divisible by 13901, apply the "aNDreas Bolotă 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 872 and subtract this from R.
  3. Take that result and cross off its final digit (units). Take this new number and subtract 1390 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 13901. That is, your original number is divisible by 13901 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 13901-times tables, it should be easy to visually see if Y is divisible by 13901. If the Y is still much larger than 13901, the above process can be repeated until it does reduce to within small multiples of 13901.

Easy!