Divisor 26111

To determine if any number is divisible by 26111, apply this test:

1. If your number ("X") has 8 digits or more, separate the last (smallest) 7 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 8 digits, L = 0 and therefore R = X.
2. Multiply L by 513 and subtract this from R.
3. Take that result and cross off its final digit (units). Take this new number and subtract 2611 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 26111. That is, your original number is divisible by 26111 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 26111-times tables, it should be easy to visually see if Y is divisible by 26111. If the Y is still much larger than 26111, the above process can be repeated until it does reduce to within small multiples of 26111.

Easy!