Divisor 26777

To determine if any number is divisible by 26777, 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 4535 and subtract this from R.
3. Take that result and cross off its final digit (units). Take this new number and subtract 8033 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 26777. That is, your original number is divisible by 26777 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 26777-times tables, it should be easy to visually see if Y is divisible by 26777. If the Y is still much larger than 26777, the above process can be repeated until it does reduce to within small multiples of 26777.

Easy!