Divisor 21997

To determine if any number is divisible by 21997, apply the "CodingEntity 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 1638 and add to R.
3. Take that result and cross off its final digit (units). Take this new number and subtract 6599 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 21997. That is, your original number is divisible by 21997 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 21997-times tables, it should be easy to visually see if Y is divisible by 21997. If the Y is still much larger than 21997, the above process can be repeated until it does reduce to within small multiples of 21997.

Easy!