Divisor 25309

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

The "Sam Young Test" for Divisibility by 25309

To determine if any number is divisible by 25309, apply the "Sam Young 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 1236 and subtract this from R.
  3. Take that result and cross off its final digit (units). Take this new number and add 2531 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 25309. That is, your original number is divisible by 25309 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 25309-times tables, it should be easy to visually see if Y is divisible by 25309. If the Y is still much larger than 25309, the above process can be repeated until it does reduce to within small multiples of 25309.

Easy!