Divisor 15971

To determine if any number is divisible by 15971, apply the "Deyan Test":

1. If your number ("X") has 11 digits or more, separate the last (smallest) 10 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 11 digits, L = 0 and therefore R = X.
2. Multiply L by 2085 and subtract this from R.
3. Take that result and cross off its final digit (units). Take this new number and subtract 1597 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 15971. That is, your original number is divisible by 15971 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 15971-times tables, it should be easy to visually see if Y is divisible by 15971. If the Y is still much larger than 15971, the above process can be repeated until it does reduce to within small multiples of 15971.

Easy!