Divisor 17359

To determine if any number is divisible by 17359, apply the "Komodo Test":

1. If your number ("X") has 10 digits or more, separate the last (smallest) 9 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 10 digits, L = 0 and therefore R = X.
2. Multiply L by 87 and add to R.
3. Take that result and cross off its final digit (units). Take this new number and add 1736 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 17359. That is, your original number is divisible by 17359 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 17359-times tables, it should be easy to visually see if Y is divisible by 17359. If the Y is still much larger than 17359, the above process can be repeated until it does reduce to within small multiples of 17359.

Easy!