Divisor 21319

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

The "Kaylee L Test" for Divisibility by 21319

To determine if any number is divisible by 21319, apply the "Kaylee L 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 1389 and add to R.
  3. Take that result and cross off its final digit (units). Take this new number and add 2132 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 21319. That is, your original number is divisible by 21319 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 21319-times tables, it should be easy to visually see if Y is divisible by 21319. If the Y is still much larger than 21319, the above process can be repeated until it does reduce to within small multiples of 21319.

Easy!