Divisor 29009

To determine if any number is divisible by 29009, apply this 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 1752 and add to R.
3. Take that result and cross off its final digit (units). Take this new number and add 2901 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 29009. That is, your original number is divisible by 29009 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 29009-times tables, it should be easy to visually see if Y is divisible by 29009. If the Y is still much larger than 29009, the above process can be repeated until it does reduce to within small multiples of 29009.

Easy!