Divisor 27893

To determine if any number is divisible by 27893, apply this test:

1. If your number ("X") has 11 digits or more, separate the last (smallest) 10 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 11 digits, L = 0 and therefore R = X.
2. Multiply L by 3109 and subtract this from R.
3. Take that result and cross off its final digit (units). Take this new number and add 8368 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 27893. That is, your original number is divisible by 27893 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 27893-times tables, it should be easy to visually see if Y is divisible by 27893. If the Y is still much larger than 27893, the above process can be repeated until it does reduce to within small multiples of 27893.

Easy!