Divisor 1307

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

The "Matthew Nanney Test" for Divisibility by 1307

To determine if any number is divisible by 1307, apply the "Matthew Nanney 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 77 and subtract this from R.
  3. Take that result and cross off its final digit (units). Take this new number and subtract 392 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 1307. That is, your original number is divisible by 1307 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 1307-times tables, it should be easy to visually see if Y is divisible by 1307. If the Y is still much larger than 1307, the above process can be repeated until it does reduce to within small multiples of 1307.

Easy!