Check Digits

Catching typos with arithmetic

An interactive lesson with 6 steps, about 5 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• Check digits make a weighted digit sum divisible by 10 (or 11).
• Single-digit typos are always detected by ISBN-13.
• Neighbour swaps differing by 5 slip through; a prime modulus (11) catches them all.

Steps

1. A built-in error detector
2. Complete the ISBN
3. One wrong digit
4. ISBN-10 check digit
5. The Luhn check
6. Swapped digits