Divisor 1187

To determine if any number is divisible by 1187, apply the "Jason Singh Test":

1. If your number ("X") has 9 digits or more, separate the last (smallest) 8 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 9 digits, L = 0 and therefore R = X.
2. Multiply L by 2 and subtract this from R.
3. Take that result and cross off its final digit (units). Take this new number and subtract 356 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 1187. That is, your original number is divisible by 1187 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 1187-times tables, it should be easy to visually see if Y is divisible by 1187. If the Y is still much larger than 1187, the above process can be repeated until it does reduce to within small multiples of 1187.

Easy!