Mathematics
The 13 Trick: Unlocking Divisibility Secrets
Quick fact
The divisibility rule for 13 works because multiplying the last digit by 4 and adding it to the rest of the number is equivalent to checking the original number modulo 13, due to the fact that 10 is congruent to -3 modulo 13, and 4 is the modular inverse of 10.
Why this is interesting
You can test if a number is divisible by 13 with a simple trick—but why does it work, and what hidden patterns make such shortcuts reliable?