Divisor 21089

To determine if any number is divisible by 21089, apply the "Adina 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 1798 and add to R.
3. Take that result and cross off its final digit (units). Take this new number and add 2109 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 21089. That is, your original number is divisible by 21089 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 21089-times tables, it should be easy to visually see if Y is divisible by 21089. If the Y is still much larger than 21089, the above process can be repeated until it does reduce to within small multiples of 21089.

Easy!