Divisor 10723
- Prime Number:
- Yes!
- Divisibility test:
- The "Treygdor Test"
- Test Discovered by:
- Matt Parker
- Date:
- 11/11/2024
The "Treygdor Test" for Divisibility by 10723
To determine if any number is divisible by 10723, apply the "Treygdor 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 1725 and subtract this from R.
- Take that result and cross off its final digit (units). Take this new number and add 3217 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 10723. That is, your original number is divisible by 10723 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 10723-times tables, it should be easy to visually see if Y is divisible by 10723. If the Y is still much larger than 10723, the above process can be repeated until it does reduce to within small multiples of 10723.
Easy!