Divisor 18013

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

The "Jan Strohbeck Test" for Divisibility by 18013

To determine if any number is divisible by 18013, apply the "Jan Strohbeck Test":

  1. If your number ("X") has 8 digits or more, separate the last (smallest) 7 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 8 digits, L = 0 and therefore R = X.
  2. Multiply L by 2785 and add to R.
  3. Take that result and cross off its final digit (units). Take this new number and add 5404 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 18013. That is, your original number is divisible by 18013 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 18013-times tables, it should be easy to visually see if Y is divisible by 18013. If the Y is still much larger than 18013, the above process can be repeated until it does reduce to within small multiples of 18013.

Easy!