Divisor 9011

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

The "Marcus Lewine Test" for Divisibility by 9011

To determine if any number is divisible by 9011, apply the "Marcus Lewine 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 221 and subtract this from R.
  3. Take that result and cross off its final digit (units). Take this new number and subtract 901 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 9011. That is, your original number is divisible by 9011 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 9011-times tables, it should be easy to visually see if Y is divisible by 9011. If the Y is still much larger than 9011, the above process can be repeated until it does reduce to within small multiples of 9011.

Easy!