Divisor 8669

To determine if any number is divisible by 8669, apply the "Timothy Morgan Test":

1. If your number ("X") has 5 digits or more, separate the last (smallest) 4 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 5 digits, L = 0 and therefore R = X.
2. Multiply L by 1331 and add to R.
3. Take that result and cross off its final digit (units). Take this new number and add 867 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 8669. That is, your original number is divisible by 8669 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 8669-times tables, it should be easy to visually see if Y is divisible by 8669. If the Y is still much larger than 8669, the above process can be repeated until it does reduce to within small multiples of 8669.

Easy!