What is a check digit?

The check digit or control digit is a way of checking, if certain numbers used for identification (Citizen Card Number; Taxpayer Identification Number; Account Bank Number) are right or wrong. This process is very usual in computer systems, which require the introduction of those numbers by hand and so it is necessary to check if there wasn't any mistake when they were digitalized.

It usually happens that the last digit, or in some cases the last two digits of the number, are the control digits. To check the number validity we make a mathematical operation with the remaining digits. If the final result is equal to the check digit, it means the number is valid.

The control algoritm is public and can be easily found through an internet search. Out of curiosity, here we have the way to check the Taxpayer Number validity whose last digit is the “check digit”. Let's look at the following example of a Taxpayer Number: 214560732.

• (d1 stands for the first digit, d2 stands for the second digit and so on)
• First step: 9 x d1 + 8 x d2 + 7 x d3 + 6 x d4 + 5 x d5 + 4 x d6 + 3 x d7 + 2 x d8
• Example: 9 x 2 + 8 x 1 + 7 x 4 + 6 x 5 + 5 x 6 + 4 x 0 + 3 x 7 + 2 x 3 = 141
• Second step: obtain the remainder of the divison by 11
• Example: 141 : 11 = 12 and the remainder is 9
• Third step: if the remainder is inferior to two, the remainder will be the “check digit”. Otherwise the “check digit” is obtained by doing: 11 - remainder
• Example: 11 - 9 = 2

Therefore, the Taxpayer Number 214560732 is valid since the number “check digit” is equal to the last digit: 2.

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