Divisor 11093

To determine if any number is divisible by 11093, apply the "Neil Fraser 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 L^eft and R^ight (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 163 and add to R.
3. Take that result and cross off its final digit (units). Take this new number and add 3328 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 11093. That is, your original number is divisible by 11093 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 11093-times tables, it should be easy to visually see if Y is divisible by 11093. If the Y is still much larger than 11093, the above process can be repeated until it does reduce to within small multiples of 11093.

Easy!