Divisor 25657

To determine if any number is divisible by 25657, apply the "Navy Test":

1. If your number ("X") has 7 digits or more, separate the last (smallest) 6 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 7 digits, L = 0 and therefore R = X.
2. Multiply L by 623 and subtract this from R.
3. Take that result and cross off its final digit (units). Take this new number and subtract 7697 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 25657. That is, your original number is divisible by 25657 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 25657-times tables, it should be easy to visually see if Y is divisible by 25657. If the Y is still much larger than 25657, the above process can be repeated until it does reduce to within small multiples of 25657.

Easy!