Divisor 7789

To determine if any number is divisible by 7789, apply the "Garrett JustGarrett Test":

1. If your number ("X") has 8 digits or more, separate the last (smallest) 7 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 8 digits, L = 0 and therefore R = X.
2. Multiply L by 1076 and subtract this from R.
3. Take that result and cross off its final digit (units). Take this new number and add 779 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 7789. That is, your original number is divisible by 7789 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 7789-times tables, it should be easy to visually see if Y is divisible by 7789. If the Y is still much larger than 7789, the above process can be repeated until it does reduce to within small multiples of 7789.

Easy!