Check digits in identification numbers are there to detect errors that happen frequently whenever one deals with numbers with many digits. These digits may be found in many daylife identification systems as, for example:

Identity Card (BI)

Tax Identification Number (NIF)


Euro bank notes

Visa card

Bank Account Number (NIB)

Check digits, despite being commonly unnoticed, are extremely useful to avoid mistakes. Have you thought what might happen in case you make a simple error while entering the NIB account number in a money transfer in a cash machine? And if a similar error happens in the reading of a barcode in the supermarket? Will the price of the product you are buying change? Check digits allow to avoid the most common errors by detecting them and alerting us.

The main idea behind these systems is mathematics, namely Modular Arithmetic. This is a fairly simple arithmetic that everybody uses for instance when checking the time on a (analogic) clock. There are also some error-detecting systems that use more advanced Group Theory. In spite of being more effective they are not much used yet.

Translated for Atractor by a CMUC team, from its original version in Portuguese. Atractor is grateful for this cooperation.

(*) This work was carried out under the guidance of Professor Jorge Picado from the Universidade of Coimbra, under a grant by the Calouste Gulbenkian Foundation to develop a project for the promotion of Mathematics in Atractor.

Difficulty level: University, Upper Secondary