Divisor 8443

To determine if any number is divisible by 8443, apply the "Luki 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 1108 and add to R.
3. Take that result and cross off its final digit (units). Take this new number and add 2533 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 8443. That is, your original number is divisible by 8443 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 8443-times tables, it should be easy to visually see if Y is divisible by 8443. If the Y is still much larger than 8443, the above process can be repeated until it does reduce to within small multiples of 8443.

Easy!