Divisor 7691

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

The "Tim Retout Test" for Divisibility by 7691

To determine if any number is divisible by 7691, apply the "Tim Retout 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 17 and add to R.
  3. Take that result and cross off its final digit (units). Take this new number and subtract 769 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 7691. That is, your original number is divisible by 7691 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 7691-times tables, it should be easy to visually see if Y is divisible by 7691. If the Y is still much larger than 7691, the above process can be repeated until it does reduce to within small multiples of 7691.

Easy!