Divisor 12143

To determine if any number is divisible by 12143, apply the "KRA2008 Test":

1. If your number ("X") has 10 digits or more, separate the last (smallest) 9 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 10 digits, L = 0 and therefore R = X.
2. Multiply L by 336 and subtract this from R.
3. Take that result and cross off its final digit (units). Take this new number and add 3643 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 12143. That is, your original number is divisible by 12143 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 12143-times tables, it should be easy to visually see if Y is divisible by 12143. If the Y is still much larger than 12143, the above process can be repeated until it does reduce to within small multiples of 12143.

Easy!