Numbers in the Real World

Chapter 4: Factoring
Numbers in the Real World

Identification Numbers

Origin of VIN Numbers Individual products are most often identified by their identification numbers. If you call to report a problem with your computer, the technician will ask for your identification number. If there is a recall on black powder rifles, the identification (serial) number will show whether your rifle may be defective. We will focus on the VIN (Vehicle Identification Number).

The VIN was introduced in its working form in 1983 as the result of a recommendation of the International Organization for Standardization ( ISO). This classification is used worldwide to identify motor vehicles, trailers, motorcycles, and mopeds.

Each VIN number is 17 characters long, with three sections. The first three digits are the WMI - World Manufacturer Identifier, the next six digits are the VDS - Vehicle Descriptor Section, and the last eight digits are the VIS - Vehicle Identifier Section.

ISO recommends that the 10th position of the VIN be the year code and the 11th position represent the factory code. All letters other than I, O, and Q are allowed, and the last four digits must be numeric.

The US, however, divides the VIN in four sections (which match up with the three sections of the ISO code):

The first three digits are the manufacturer code (WMI).
The next five digits identify the attributes of the vehicle (VDS).
The next digit is the check digit, an arithmetic check for the other 16 characters. It may be numeric or the letter X.
The last eight digits are like the VIS above.

Below is a VIN from a Ford Mustang.

1FA CP45E X LF192944
WMI VDS VIS

Purpose of Check Digit in VIN Numbers

A numerical value is assigned to each letter:

A=1	F=6	L=3	S=2	X=7
B=2	G=7	M=4	T=3	Y=8/TD>
C=3	H=8	N=5	U=4	Z=9
D=4	J=1	P=7	V=5
E=5	K=2	R=9	W=6

A weight value is assigned to each position:

1st=8	5th=4	10th=9	14th=5
2nd=7	6th=3	11th=8	15th=4
3rd=6	7th=2	12th=7	16th=3
4th=5	8th=10	13th=6	17th=2

Multiply the numerical value and weight value for each character in each position and add those products. Then divide that sum by 11 and consider the remainder. The remainder is the check digit unless the remainder is 10, in which case the letter X is the check digit.

Application of VIN Numbers

Insurance companies, police stations, banks, and car dealerships have a safeguard against entering the wrong VIN number or accepting a false one. Here are some examples.

The VIN number that was provided on an auto loan application is 1B4YEM9P4KP186543.
What is the sum? Is it a valid VIN number?

Police found an abandoned car. In order to locate the owner, they took down the VIN number 1FA_GB4AX34134587.
However, the fourth digit was difficult to read. It was either a 6 or a b. Which digit is correct?

Check Your Answers