Divisor 1213

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

The "Eli Kaituri Test" for Divisibility by 1213

To determine if any number is divisible by 1213, apply the "Eli Kaituri Test":

  1. If your number ("X") has 8 digits or more, separate the last (smallest) 7 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 8 digits, L = 0 and therefore R = X.
  2. Multiply L by 28 and add to R.
  3. Take that result and cross off its final digit (units). Take this new number and add 364 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 1213. That is, your original number is divisible by 1213 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 1213-times tables, it should be easy to visually see if Y is divisible by 1213. If the Y is still much larger than 1213, the above process can be repeated until it does reduce to within small multiples of 1213.

Easy!