Divisor 1567

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

The "Jared Necaise Test" for Divisibility by 1567

To determine if any number is divisible by 1567, apply the "Jared Necaise 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 146 and add to R.
  3. Take that result and cross off its final digit (units). Take this new number and subtract 470 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 1567. That is, your original number is divisible by 1567 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 1567-times tables, it should be easy to visually see if Y is divisible by 1567. If the Y is still much larger than 1567, the above process can be repeated until it does reduce to within small multiples of 1567.

Easy!