Divisor 16519

To determine if any number is divisible by 16519, apply the "Jan Test":

1. If your number ("X") has 6 digits or more, separate the last (smallest) 5 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 6 digits, L = 0 and therefore R = X.
2. Multiply L by 886 and add to R.
3. Take that result and cross off its final digit (units). Take this new number and add 1652 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 16519. That is, your original number is divisible by 16519 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 16519-times tables, it should be easy to visually see if Y is divisible by 16519. If the Y is still much larger than 16519, the above process can be repeated until it does reduce to within small multiples of 16519.

Easy!