Divisor 21757

To determine if any number is divisible by 21757, apply the "Martin Test":

1. If your number ("X") has 7 digits or more, separate the last (smallest) 6 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 7 digits, L = 0 and therefore R = X.
2. Multiply L by 822 and subtract this from R.
3. Take that result and cross off its final digit (units). Take this new number and subtract 6527 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 21757. That is, your original number is divisible by 21757 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 21757-times tables, it should be easy to visually see if Y is divisible by 21757. If the Y is still much larger than 21757, the above process can be repeated until it does reduce to within small multiples of 21757.

Easy!