Divisor 23971

Prime Number:
Yes!
Divisibility test:
The "Elmer A. Johnsen Test"
Test Discovered by:
Matt Parker
Date:
11/11/2024

The "Elmer A. Johnsen Test" for Divisibility by 23971

To determine if any number is divisible by 23971, apply the "Elmer A. Johnsen 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 1793 and add to R.
  3. Take that result and cross off its final digit (units). Take this new number and subtract 2397 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 23971. That is, your original number is divisible by 23971 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 23971-times tables, it should be easy to visually see if Y is divisible by 23971. If the Y is still much larger than 23971, the above process can be repeated until it does reduce to within small multiples of 23971.

Easy!