Divisor 15823

To determine if any number is divisible by 15823, apply the "Alex 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 136 and subtract this from R.
3. Take that result and cross off its final digit (units). Take this new number and add 4747 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 15823. That is, your original number is divisible by 15823 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 15823-times tables, it should be easy to visually see if Y is divisible by 15823. If the Y is still much larger than 15823, the above process can be repeated until it does reduce to within small multiples of 15823.

Easy!