THE CHECK DIGIT SYSTEM – Identification numbers for documents, accounts, products and services that
include a self – checking system for detecting errors.
US Postal Money Orders
10 digits followed by the check digit a1a2a3a4a5a6a7a8a9a10C
The check digit, C, is the remainder when the sum of the first 10 digits is divided by 9.
( sum of 1st 10 digits)  C (mod 9)
American Express Traveler’s Cheques, VISA Traveler’s Cheques, &
Euro Bank notes
The sum of the digits including the check digit is divisible by 9.
( sum of digits)  0 (mod 9)
Airline Tickets, UPS Packages, and Avis and National Rental Cars
The NUMBER itself is divided by 7. The check digit is the remainder.
NUMBER  C (mod 7)
UPC or Universal Product Codes
A twelve digit number - 11 digits followed by the check digit: a1a2a3a4a5a6a7a8a9a10 a11C
The computer assigns “weights” to alternating digits by multiplying as follows
3a1+ 1a2 + 3 a3 +1 a4 + 3a5 + 1a6 + 3 a7 + 1 a8 +3a9 + 1a10 + 3 a11 +1 C
The check digit, C, is assigned such that the above sum ends in a zero.
(3a1  1a 2  3 a 3  1 a 4  3a 5  1a 6  3a 7  1 a 8 3a 9  1a10  3 a11  1 C)  0 mod 10
BANKING
An eight digit routing number followed by a check digit: a1a2a3a4a5a6a7a8C
The computer assigns “weights” to alternating digits by multiplying as follows
7a1+ 3a2 + 9 a3 + 7 a4 + 3a5 + 9a6 + 7 a7 + 3 a8
The check digit, C, is the remainder when the above sum is divided by 10.
(7a1  3a 2  9 a 3  7 a 4  3a 5  9a 6  7 a 7  3 a 8 )  C mod 10