Clock Arithmetic

Remainders that wrap around

An interactive lesson with 7 steps, about 6 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• $a \equiv b \pmod n$ means $a$ and $b$ leave the same remainder after dividing by $n$.
• Reduce early: you can add and multiply in modular arithmetic.
• Powers repeat in cycles mod n, which makes huge powers easy.

Steps

1. What time will it be?
2. Mod
3. Jumping around a clock
4. Times tables on a circle
5. Day of the week
6. Last digit of a huge power
7. Remainder of a giant