Divisor 7949

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

The "Paul Smith Test" for Divisibility by 7949

To determine if any number is divisible by 7949, apply the "Paul Smith Test":

  1. If your number ("X") has 10 digits or more, separate the last (smallest) 9 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 10 digits, L = 0 and therefore R = X.
  2. Multiply L by 98 and subtract this from R.
  3. Take that result and cross off its final digit (units). Take this new number and add 795 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 7949. That is, your original number is divisible by 7949 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 7949-times tables, it should be easy to visually see if Y is divisible by 7949. If the Y is still much larger than 7949, the above process can be repeated until it does reduce to within small multiples of 7949.

Easy!