Divisor 28723

To determine if any number is divisible by 28723, 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 1381 and add to R.
3. Take that result and cross off its final digit (units). Take this new number and add 8617 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 28723. That is, your original number is divisible by 28723 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 28723-times tables, it should be easy to visually see if Y is divisible by 28723. If the Y is still much larger than 28723, the above process can be repeated until it does reduce to within small multiples of 28723.

Easy!