Divisor 16603

Prime Number:
Yes!
Divisibility test:
The "Jason Sherman Test"
Test Discovered by:
Matt Parker
Date:
11/11/2024

The "Jason Sherman Test" for Divisibility by 16603

To determine if any number is divisible by 16603, apply the "Jason Sherman Test":

  1. If your number ("X") has 9 digits or more, separate the last (smallest) 8 digits from the rest. This makes two smaller numbers, call them Left and Right (note: don't add in trailing zeros to L). If there are fewer than 9 digits, L = 0 and therefore R = X.
  2. Multiply L by 131 and add to R.
  3. Take that result and cross off its final digit (units). Take this new number and add 4981 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 16603. That is, your original number is divisible by 16603 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 16603-times tables, it should be easy to visually see if Y is divisible by 16603. If the Y is still much larger than 16603, the above process can be repeated until it does reduce to within small multiples of 16603.

Easy!