Divisor 3967

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

The "Carl Löfgren Test" for Divisibility by 3967

To determine if any number is divisible by 3967, apply the "Carl Löfgren 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 136 and subtract this from R.
  3. Take that result and cross off its final digit (units). Take this new number and subtract 1190 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 3967. That is, your original number is divisible by 3967 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 3967-times tables, it should be easy to visually see if Y is divisible by 3967. If the Y is still much larger than 3967, the above process can be repeated until it does reduce to within small multiples of 3967.

Easy!