Divisor 4801

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

The "William Clark Test" for Divisibility by 4801

To determine if any number is divisible by 4801, apply the "William Clark 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 29 and subtract this from R.
  3. Take that result and cross off its final digit (units). Take this new number and subtract 480 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 4801. That is, your original number is divisible by 4801 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 4801-times tables, it should be easy to visually see if Y is divisible by 4801. If the Y is still much larger than 4801, the above process can be repeated until it does reduce to within small multiples of 4801.

Easy!