Divisor 6701

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

The "stephenjfisk Test" for Divisibility by 6701

To determine if any number is divisible by 6701, apply the "stephenjfisk 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 515 and subtract this from R.
  3. Take that result and cross off its final digit (units). Take this new number and subtract 670 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 6701. That is, your original number is divisible by 6701 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 6701-times tables, it should be easy to visually see if Y is divisible by 6701. If the Y is still much larger than 6701, the above process can be repeated until it does reduce to within small multiples of 6701.

Easy!