Divisor 25457

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

The "Emlyn Test" for Divisibility by 25457

To determine if any number is divisible by 25457, apply the "Emlyn 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 1828 and subtract this from R.
  3. Take that result and cross off its final digit (units). Take this new number and subtract 7637 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 25457. That is, your original number is divisible by 25457 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 25457-times tables, it should be easy to visually see if Y is divisible by 25457. If the Y is still much larger than 25457, the above process can be repeated until it does reduce to within small multiples of 25457.

Easy!