Divisor 3623

To determine if any number is divisible by 3623, apply the "Chad James 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 52 and add to R.
3. Take that result and cross off its final digit (units). Take this new number and add 1087 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 3623. That is, your original number is divisible by 3623 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 3623-times tables, it should be easy to visually see if Y is divisible by 3623. If the Y is still much larger than 3623, the above process can be repeated until it does reduce to within small multiples of 3623.

Easy!