Divisor 14009

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

The "Colin Chan Test" for Divisibility by 14009

To determine if any number is divisible by 14009, apply the "Colin Chan 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 1937 and add to R.
  3. Take that result and cross off its final digit (units). Take this new number and add 1401 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 14009. That is, your original number is divisible by 14009 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 14009-times tables, it should be easy to visually see if Y is divisible by 14009. If the Y is still much larger than 14009, the above process can be repeated until it does reduce to within small multiples of 14009.

Easy!