Divisor 19751

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

The "Robert Gendron Test" for Divisibility by 19751

To determine if any number is divisible by 19751, apply the "Robert Gendron Test":

  1. If your number ("X") has 9 digits or more, separate the last (smallest) 8 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 9 digits, L = 0 and therefore R = X.
  2. Multiply L by 687 and add to R.
  3. Take that result and cross off its final digit (units). Take this new number and subtract 1975 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 19751. That is, your original number is divisible by 19751 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 19751-times tables, it should be easy to visually see if Y is divisible by 19751. If the Y is still much larger than 19751, the above process can be repeated until it does reduce to within small multiples of 19751.

Easy!