Divisor 20593

To determine if any number is divisible by 20593, apply the "Alex K. Test":

1. If your number ("X") has 9 digits or more, separate the last (smallest) 8 digits from the rest. This makes two smaller numbers, call them L^eft and R^ight (note: don't add in trailing zeros to L). If there are fewer than 9 digits, L = 0 and therefore R = X.
2. Multiply L by 392 and add to R.
3. Take that result and cross off its final digit (units). Take this new number and add 6178 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 20593. That is, your original number is divisible by 20593 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 20593-times tables, it should be easy to visually see if Y is divisible by 20593. If the Y is still much larger than 20593, the above process can be repeated until it does reduce to within small multiples of 20593.

Easy!