Divisor 21727

To determine if any number is divisible by 21727, apply the "mike Test":

1. If your number ("X") has 7 digits or more, separate the last (smallest) 6 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 7 digits, L = 0 and therefore R = X.
2. Multiply L by 558 and add to R.
3. Take that result and cross off its final digit (units). Take this new number and subtract 6518 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 21727. That is, your original number is divisible by 21727 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 21727-times tables, it should be easy to visually see if Y is divisible by 21727. If the Y is still much larger than 21727, the above process can be repeated until it does reduce to within small multiples of 21727.

Easy!