Divisor 20641

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

The "Shahin Test" for Divisibility by 20641

To determine if any number is divisible by 20641, apply the "Shahin Test":

  1. If your number ("X") has 6 digits or more, separate the last (smallest) 5 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 6 digits, L = 0 and therefore R = X.
  2. Multiply L by 3205 and subtract this from R.
  3. Take that result and cross off its final digit (units). Take this new number and subtract 2064 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 20641. That is, your original number is divisible by 20641 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 20641-times tables, it should be easy to visually see if Y is divisible by 20641. If the Y is still much larger than 20641, the above process can be repeated until it does reduce to within small multiples of 20641.

Easy!