Divisor 7219

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

The "Ben Cooper Test" for Divisibility by 7219

To determine if any number is divisible by 7219, apply the "Ben Cooper 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 1066 and subtract this from R.
  3. Take that result and cross off its final digit (units). Take this new number and add 722 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 7219. That is, your original number is divisible by 7219 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 7219-times tables, it should be easy to visually see if Y is divisible by 7219. If the Y is still much larger than 7219, the above process can be repeated until it does reduce to within small multiples of 7219.

Easy!