Divisor 27941

To determine if any number is divisible by 27941, 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 77 and subtract this from R.
3. Take that result and cross off its final digit (units). Take this new number and subtract 2794 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 27941. That is, your original number is divisible by 27941 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 27941-times tables, it should be easy to visually see if Y is divisible by 27941. If the Y is still much larger than 27941, the above process can be repeated until it does reduce to within small multiples of 27941.

Easy!