Check Credit Card Digit

Credit cards numbers use check digits to guard against mistakes and to check for validity. In the section the credit cards MasterCard, VISA, American Express, and Discover will be considered. All of these cards use the same format for determining and verifying check digits.

Why have a check digit in a credit card number?:

• It can determine if a person keys in a number incorrectly
• If  a credit card is scanned it can determine of the scanner made a mistake

When dealing with credit cards it is important to realize that some have different lengths and have different prefixs.

• MasterCard is of length 16 and has a prefix of 51, 52, 53, 54, 55
• VISA is of length 13 or 16 and has a prefix of 4
• American Express is of length 15 and has a prefix of 34 or 37
• Discover is of length 16 and has a prefix of 6011

All of the above credits use (mod 10) to determine a check digit, and in all cases the check digit is the right-most digit in the number. To determine the check digit for a credit card follow the below steps.

NOTE: In MasterCard and VISA include the prefix digits in the calculation. In American Express and Discover the prefix digits are omitted from all calculations.

NOTE: For the below example we consider a random possible MasterCard number 5368235896831135.

Step 1: Starting from the second digit from the right and moving towards the left, multiply every digit by 2.

3*2 = 6
1*2 = 2
8*2 = 16
9*2 = 18
5*2 = 10
2*2 = 4
6*2 = 12
5*2 = 10

Step 2: Sum the digits from Step 1.

6 + 2 + 1 + 6 + 1 + 8 + 1 + 0 + 4 + 1 + 2 + 1 + 0 = 33

Step 3: Sum all of the digits not originally mutliplied by 2.

3 + 8 + 3 + 8 + 6 + 3 + 1 = 32

Step 4: Sum together the results from Step 2 and Step 3.

33 + 32 = 55

Step 5: Subtract the sum from the next highest multiple of 10.

60 -55 = 5 [check digit]

A person can determine if the check digit  of a given credit card is valid by   repeating Steps 1, 2, 3, 4 above for all digits, including the check digit. The sum, s, obtained in Step 4 should  be s = 0(mod 10). In our case 60 = 0 (mod 10).

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