Divisor 10691
- Prime Number:
- Yes!
- Divisibility test:
- The "Aaron Ferrucci Test"
- Test Discovered by:
- Matt Parker
- Date:
- 11/11/2024
The "Aaron Ferrucci Test" for Divisibility by 10691
To determine if any number is divisible by 10691, apply the "Aaron Ferrucci Test":
- If your number ("X") has 11 digits or more, separate the last (smallest) 10 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 11 digits, L = 0 and therefore R = X.
- Multiply L by 2094 and add to R.
- Take that result and cross off its final digit (units). Take this new number and subtract 1069 times the digit you just crossed off. Call this final result "Y".
- Y will be much smaller than X, but we have preserved divisibility by 10691. That is, your original number is divisible by 10691 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 10691-times tables, it should be easy to visually see if Y is divisible by 10691. If the Y is still much larger than 10691, the above process can be repeated until it does reduce to within small multiples of 10691.
Easy!