Divisor 2339

To determine if any number is divisible by 2339, apply the "Kevin Steegmann 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 313 and add to R.
3. Take that result and cross off its final digit (units). Take this new number and add 234 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 2339. That is, your original number is divisible by 2339 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 2339-times tables, it should be easy to visually see if Y is divisible by 2339. If the Y is still much larger than 2339, the above process can be repeated until it does reduce to within small multiples of 2339.

Easy!