Divisor 20981

To determine if any number is divisible by 20981, apply the "Morgan Phillips 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 3578 and add to R.
3. Take that result and cross off its final digit (units). Take this new number and subtract 2098 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 20981. That is, your original number is divisible by 20981 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 20981-times tables, it should be easy to visually see if Y is divisible by 20981. If the Y is still much larger than 20981, the above process can be repeated until it does reduce to within small multiples of 20981.

Easy!