Divisor 9907
- Prime Number:
- Yes!
- Divisibility test:
- The "Paul Collins Test"
- Test Discovered by:
- Matt Parker
- Date:
- 11/11/2024
The "Paul Collins Test" for Divisibility by 9907
To determine if any number is divisible by 9907, apply the "Paul Collins Test":
- If your number ("X") has 5 digits or more, separate the last (smallest) 4 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 5 digits, L = 0 and therefore R = X.
- Multiply L by 93 and add to R.
- Take that result and cross off its final digit (units). Take this new number and subtract 2972 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 9907. That is, your original number is divisible by 9907 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 9907-times tables, it should be easy to visually see if Y is divisible by 9907. If the Y is still much larger than 9907, the above process can be repeated until it does reduce to within small multiples of 9907.
Easy!