Divisor 15671

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

The "James Cahill Test" for Divisibility by 15671

To determine if any number is divisible by 15671, apply the "James Cahill Test":

  1. If your number ("X") has 8 digits or more, separate the last (smallest) 7 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 8 digits, L = 0 and therefore R = X.
  2. Multiply L by 1902 and add to R.
  3. Take that result and cross off its final digit (units). Take this new number and subtract 1567 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 15671. That is, your original number is divisible by 15671 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 15671-times tables, it should be easy to visually see if Y is divisible by 15671. If the Y is still much larger than 15671, the above process can be repeated until it does reduce to within small multiples of 15671.

Easy!