Divisor 16129

To determine if any number is divisible by 16129, apply this test:

1. If your number ("X") has 7 digits or more, separate the last (smallest) 6 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 7 digits, L = 0 and therefore R = X.
2. Multiply L by 2 and add to R.
3. Take that result and cross off its final digit (units). Take this new number and add 1613 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 16129. That is, your original number is divisible by 16129 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 16129-times tables, it should be easy to visually see if Y is divisible by 16129. If the Y is still much larger than 16129, the above process can be repeated until it does reduce to within small multiples of 16129.

Easy!