Follow your curiosity

What discovery has been shared with you?

FACTREE gives you something interesting to discover every day — and something worth talking about together.

Start with one fact. Explore it, go deeper, then follow whichever branch catches your imagination.

Choose subjects for a surprise

Exploring any topic

Begin your discovery

Your next discovery is one click away.

Choose one or more subjects above, or leave Any Topic selected and let curiosity decide.

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?