Divisor 19321

To determine if any number is divisible by 19321, apply this 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 3003 and add to R.
3. Take that result and cross off its final digit (units). Take this new number and subtract 1932 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 19321. That is, your original number is divisible by 19321 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 19321-times tables, it should be easy to visually see if Y is divisible by 19321. If the Y is still much larger than 19321, the above process can be repeated until it does reduce to within small multiples of 19321.

Easy!