Divisor 5807

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

The "David McLean Test" for Divisibility by 5807

To determine if any number is divisible by 5807, apply the "David McLean Test":

  1. If your number ("X") has 10 digits or more, separate the last (smallest) 9 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 10 digits, L = 0 and therefore R = X.
  2. Multiply L by 242 and subtract this from R.
  3. Take that result and cross off its final digit (units). Take this new number and subtract 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 5807. That is, your original number is divisible by 5807 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 5807-times tables, it should be easy to visually see if Y is divisible by 5807. If the Y is still much larger than 5807, the above process can be repeated until it does reduce to within small multiples of 5807.

Easy!