Divisor 21577

Prime Number:
Yes!
Divisibility test:
The "John-Carlo Ricciardi Test"
Test Discovered by:
Matt Parker
Date:
11/11/2024

The "John-Carlo Ricciardi Test" for Divisibility by 21577

To determine if any number is divisible by 21577, apply the "John-Carlo Ricciardi 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 7458 and add to R.
  3. Take that result and cross off its final digit (units). Take this new number and subtract 6473 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 21577. That is, your original number is divisible by 21577 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 21577-times tables, it should be easy to visually see if Y is divisible by 21577. If the Y is still much larger than 21577, the above process can be repeated until it does reduce to within small multiples of 21577.

Easy!