Name: ____________________________________________________________________ Date _____________
Discrete Math II: 16.1 – Check Digits (Page 6a)
A) Money Orders: sum the non-check digits and divide by 9; CD is the remainder
B) Travelers’ Checks: sum including CD is evenly divisible by 9
C) Airline Tickets, Rental Cars: divide the number without the CD by 7; CD is the
remainder
D) UPCs: calculate weight of 3,1. CD is what adds to it to make it end in 0
E) Bank Routing #s: calculate weight of 7, 3, 9 without CD. CD is the
last digit of the sum.
F) Credit Card Numbers – calculate weight of 2, 1. Add to it # of digits with weight of 2 > 4;
CD is what adds to it to make it end in 0
G) Book Numbers (10-Digit ISBN): calculate [10(1st) + 9(2nd) + 8(3rd) + 7(4th) + 6(5th) + 5(6th) +
4(7th) + 3(8th) + 2(9th)] plus CD is evenly divisible by 11.
H) Book Numbers (13-Digit ISBN): weight of 1, 3; CD is what
adds to it to make it end in 0
1. Find check digits for the following ID’s:
a) Traveler’s Check #: 3146 2211 ___
b) UPC #: 3 18600 81425 ___
c) 10-Digit ISBN #: 1-6857-1149 ___
d) Rental Car #: 812014 ___
e) Credit Card #: 4313 0753 6380 613 ___
f) Bank Routing #: 1824 3209 ___
g) 13-Digit ISBN #: 978-1-6841-2047 ___
h) Money Order #: 21645 13485 ___
i) Airline Ticket #: 053211 ___
j) Credit Card #: 1806 8580 1925 007 ___
Discrete Math II: 16.1 – Check Digits (Page 6b)
A) Money Orders: sum the non-check digits and divide by 9; CD is the remainder
B) Travelers’ Checks: sum including CD is evenly divisible by 9
C) Airline Tickets, Rental Cars: divide the number without the CD by 7; CD is the
remainder
D) UPCs: calculate weight of 3,1. CD is what adds to it to make it end in 0
E) Bank Routing #s: calculate weight of 7, 3, 9 without CD. CD is the
last digit of the sum.
F) Credit Card Numbers – calculate weight of 2, 1. Add to it # of digits with weight of 2 > 4;
CD is what adds to it to make it end in 0
G) Book Numbers (10-Digit ISBN): calculate [10(1st) + 9(2nd) + 8(3rd) + 7(4th) + 6(5th) + 5(6th) +
4(7th) + 3(8th) + 2(9th)] plus CD is evenly divisible by 11.
H) Book Numbers (13-Digit ISBN): weight of 1, 3; CD is what
adds to it to make it end in 0
2. Determine if the following ID’s are valid:
a) Bank Routing #: 8124 0381 1
b) 13-Digit ISBN #: 978-1-1045-9667 5
c) 10-Digit ISBN #: 2-3196-0743 8
d) Rental Car #: 035914 4
e) Airline Ticket #: 1045392 6
f) Money Order #: 43121 68704 3
g) Credit Card #: 1874 3319 6872 858 4
h) Traveler’s Check #: 3890 2016 7
i) UPC #: 4 12560 31198 3
j) 13-Digit ISBN #: 979-2-0014-8116 8