Divisor 18461

To determine if any number is divisible by 18461, apply the "Jazzmanic 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 3106 and add to R.
3. Take that result and cross off its final digit (units). Take this new number and subtract 1846 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 18461. That is, your original number is divisible by 18461 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 18461-times tables, it should be easy to visually see if Y is divisible by 18461. If the Y is still much larger than 18461, the above process can be repeated until it does reduce to within small multiples of 18461.

Easy!