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## A Practical Example

Most of the long number strings we deal with every day (credit card numbers, IMEI numbers in your phone, and so on) have a check digit. This is normally the final digit of the number, and it is calculated using some algorithm that combines all the previous digits. So, when you enter your credit card number, the web page can recalculate the check digit, and verify that it is the same as the last digit in the number you gave. It isn’t a check against fraud; it’s simply a quick way of picking up typos.

Probably the most widely used technique is the Luhn Algorithm.[5] It reverses the digits in the number, and splits them into two sets: digits at odd positions in the string, and digits at even positions. It sums the odd digits. ...

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