Divisor 10909

To determine if any number is divisible by 10909, apply the "Jeremy 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 1819 and add to R.
3. Take that result and cross off its final digit (units). Take this new number and add 1091 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 10909. That is, your original number is divisible by 10909 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 10909-times tables, it should be easy to visually see if Y is divisible by 10909. If the Y is still much larger than 10909, the above process can be repeated until it does reduce to within small multiples of 10909.

Easy!