Divisor 5651

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

The "Heather Liu Test" for Divisibility by 5651

To determine if any number is divisible by 5651, apply the "Heather Liu 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 96 and subtract this from R.
  3. Take that result and cross off its final digit (units). Take this new number and subtract 565 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 5651. That is, your original number is divisible by 5651 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 5651-times tables, it should be easy to visually see if Y is divisible by 5651. If the Y is still much larger than 5651, the above process can be repeated until it does reduce to within small multiples of 5651.

Easy!