Divisor 2731

To determine if any number is divisible by 2731, apply the "PerfectlyAdequate 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 454 and add to R.
3. Take that result and cross off its final digit (units). Take this new number and subtract 273 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 2731. That is, your original number is divisible by 2731 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 2731-times tables, it should be easy to visually see if Y is divisible by 2731. If the Y is still much larger than 2731, the above process can be repeated until it does reduce to within small multiples of 2731.

Easy!