Divisor 10357

To determine if any number is divisible by 10357, apply the "r10pez10 Test":

1. If your number ("X") has 10 digits or more, separate the last (smallest) 9 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 10 digits, L = 0 and therefore R = X.
2. Multiply L by 579 and add to R.
3. Take that result and cross off its final digit (units). Take this new number and subtract 3107 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 10357. That is, your original number is divisible by 10357 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 10357-times tables, it should be easy to visually see if Y is divisible by 10357. If the Y is still much larger than 10357, the above process can be repeated until it does reduce to within small multiples of 10357.

Easy!