Divisor 16657

Prime Number:
Yes!
Divisibility test:
The "RoeRB211 Test"
Test Discovered by:
Matt Parker
Date:
11/11/2024

The "RoeRB211 Test" for Divisibility by 16657

To determine if any number is divisible by 16657, apply the "RoeRB211 Test":

  1. If your number ("X") has 6 digits or more, separate the last (smallest) 5 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 6 digits, L = 0 and therefore R = X.
  2. Multiply L by 58 and add to R.
  3. Take that result and cross off its final digit (units). Take this new number and subtract 4997 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 16657. That is, your original number is divisible by 16657 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 16657-times tables, it should be easy to visually see if Y is divisible by 16657. If the Y is still much larger than 16657, the above process can be repeated until it does reduce to within small multiples of 16657.

Easy!