How the MOD 10 Algorithm Works

Published March 21st, 2013

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 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".