Divisor 17959

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

The "William Q Test" for Divisibility by 17959

To determine if any number is divisible by 17959, apply the "William Q Test":

  1. If your number ("X") has 11 digits or more, separate the last (smallest) 10 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 11 digits, L = 0 and therefore R = X.
  2. Multiply L by 2216 and subtract this from R.
  3. Take that result and cross off its final digit (units). Take this new number and add 1796 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 17959. That is, your original number is divisible by 17959 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 17959-times tables, it should be easy to visually see if Y is divisible by 17959. If the Y is still much larger than 17959, the above process can be repeated until it does reduce to within small multiples of 17959.

Easy!