Divisor 19739

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

The "Henry Segerman Test" for Divisibility by 19739

To determine if any number is divisible by 19739, apply the "Henry Segerman 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 1305 and add to R.
  3. Take that result and cross off its final digit (units). Take this new number and add 1974 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 19739. That is, your original number is divisible by 19739 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 19739-times tables, it should be easy to visually see if Y is divisible by 19739. If the Y is still much larger than 19739, the above process can be repeated until it does reduce to within small multiples of 19739.

Easy!