Divisor 17

To determine if any number is divisible by 17, apply this test:

1. If your number ("X") has 3 digits or more, separate the last (smallest) 2 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 3 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 5 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 17. That is, your original number is divisible by 17 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 17-times tables, it should be easy to visually see if Y is divisible by 17. If the Y is still much larger than 17, the above process can be repeated until it does reduce to within small multiples of 17.

Easy!