Divisor 7753

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

The "Paige Gulley Test" for Divisibility by 7753

To determine if any number is divisible by 7753, apply the "Paige Gulley Test":

  1. If your number ("X") has 7 digits or more, separate the last (smallest) 6 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 7 digits, L = 0 and therefore R = X.
  2. Multiply L by 137 and subtract this from R.
  3. Take that result and cross off its final digit (units). Take this new number and add 2326 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 7753. That is, your original number is divisible by 7753 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 7753-times tables, it should be easy to visually see if Y is divisible by 7753. If the Y is still much larger than 7753, the above process can be repeated until it does reduce to within small multiples of 7753.

Easy!