How the MOD 10 Algorithm Works

Published March 21st, 2013 at 11:35 AM. by Joe Prochazka


The following is an explanation of how the MOD 10 algorithm works. This information is useful if you wish to validate a credit card number more thoroughly than just looking for what numbers a credit card starts with and/or it’s length. It is also useful if only to better understand how credit card numbers are created. First we will start with a bogus number generated using the algorithm.

Bogus But "Valid" Card Number = 378282246310005

Next we will flip the card number around.

Flip Card Number = 500013642282873

Now we need to double the value for every second digit. If during the multiplication you get a double digit number add the two numbers together so if you come up with say 14 the correct value for this would be 1+4 which makes the value 5. (14 = 1+4=5)

Double the value of every second digit = 0068445

Now replace the multiplied numbers within the flipped card number.

Number after replacing every other number = 500016682484853

Next add the first and second digits together.

Total of first and second digit = 5+0=5

Now add the next two together.

Sum of the next two digits = 0+0=0

Repeat this process until you reach the end of the string.

Sum up the rest of the numbers = 1+6=7, 6+8=14, 2+4=6, 4+8=12, 8+5=13, 3+nothing=3

Then add the resulting numbers together.

5+0+7+14+6+12+13+3 = 60

In order for the number to pass the remainder must be equal to 0.

60 MOD 10 = 0 (10 goes into 60 6 times with no remainder)

The result is that the number is "good".


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