Divisor 15319

To determine if any number is divisible by 15319, apply the "Ugore 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 1904 and add to R.
3. Take that result and cross off its final digit (units). Take this new number and add 1532 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 15319. That is, your original number is divisible by 15319 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 15319-times tables, it should be easy to visually see if Y is divisible by 15319. If the Y is still much larger than 15319, the above process can be repeated until it does reduce to within small multiples of 15319.

Easy!