Divisor 22621

To determine if any number is divisible by 22621, apply the "Joost Test":

1. If your number ("X") has 8 digits or more, separate the last (smallest) 7 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 8 digits, L = 0 and therefore R = X.
2. Multiply L by 1518 and add to R.
3. Take that result and cross off its final digit (units). Take this new number and subtract 2262 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 22621. That is, your original number is divisible by 22621 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 22621-times tables, it should be easy to visually see if Y is divisible by 22621. If the Y is still much larger than 22621, the above process can be repeated until it does reduce to within small multiples of 22621.

Easy!