Divisor 7639

To determine if any number is divisible by 7639, apply the "Reign 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 549 and add to R.
3. Take that result and cross off its final digit (units). Take this new number and add 764 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 7639. That is, your original number is divisible by 7639 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 7639-times tables, it should be easy to visually see if Y is divisible by 7639. If the Y is still much larger than 7639, the above process can be repeated until it does reduce to within small multiples of 7639.

Easy!