Divisor 4547

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

The "Benjamin Nelson Test" for Divisibility by 4547

To determine if any number is divisible by 4547, apply the "Benjamin Nelson 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 34 and subtract this from R.
  3. Take that result and cross off its final digit (units). Take this new number and subtract 1364 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 4547. That is, your original number is divisible by 4547 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 4547-times tables, it should be easy to visually see if Y is divisible by 4547. If the Y is still much larger than 4547, the above process can be repeated until it does reduce to within small multiples of 4547.

Easy!