Divisor 6971

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

The "Bart Zonneveld Test" for Divisibility by 6971

To determine if any number is divisible by 6971, apply the "Bart Zonneveld 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 1005 and add to R.
  3. Take that result and cross off its final digit (units). Take this new number and subtract 697 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 6971. That is, your original number is divisible by 6971 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 6971-times tables, it should be easy to visually see if Y is divisible by 6971. If the Y is still much larger than 6971, the above process can be repeated until it does reduce to within small multiples of 6971.

Easy!