Divisor 17419

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

The "Richard Breen Test" for Divisibility by 17419

To determine if any number is divisible by 17419, apply the "Richard Breen Test":

  1. If your number ("X") has 8 digits or more, separate the last (smallest) 7 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 8 digits, L = 0 and therefore R = X.
  2. Multiply L by 1494 and add to R.
  3. Take that result and cross off its final digit (units). Take this new number and add 1742 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 17419. That is, your original number is divisible by 17419 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 17419-times tables, it should be easy to visually see if Y is divisible by 17419. If the Y is still much larger than 17419, the above process can be repeated until it does reduce to within small multiples of 17419.

Easy!