Divisor 12809

To determine if any number is divisible by 12809, apply the "Dysnomia 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 137 and add to R.
3. Take that result and cross off its final digit (units). Take this new number and add 1281 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 12809. That is, your original number is divisible by 12809 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 12809-times tables, it should be easy to visually see if Y is divisible by 12809. If the Y is still much larger than 12809, the above process can be repeated until it does reduce to within small multiples of 12809.

Easy!