Divisor 7457

To determine if any number is divisible by 7457, apply the "Ganon11 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 163 and add to R.
3. Take that result and cross off its final digit (units). Take this new number and subtract 2237 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 7457. That is, your original number is divisible by 7457 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 7457-times tables, it should be easy to visually see if Y is divisible by 7457. If the Y is still much larger than 7457, the above process can be repeated until it does reduce to within small multiples of 7457.

Easy!