ISBN-10 Validity

Have you ever looked at the back of a book and above the barcode there is a number? Well, that is how books are classified internationally. Prior to 2007, ISBN-10 (International Standard Book Number) was standard. With it now being phased out, ISBN-13 has taken its spot! ISBN-10 is still common today, with books being published with both ISBN-10 and ISBN-13 on the back! Did you also know that the validity of ISBN-10 can be figured out by math? I would like to show you how! For this example, we will be using this ISBN-10.

ISBN-10: 1-932698-18-3

To figure out if an ISBN-10 number is valid you have to follow these steps!

First, write down the whole ISBN-10 number.


Remove the dashes.


Second, similar to UPCs, Bank Routing Numbers, and Money Orders, you have to multiply the ISBN-10 by the weight!

In ISBN-10, The weight is: 10,9,8,7,6,5,4,3,2,1.

(I will put it in a grid to make it easier to visualize)

1 *10 10
9 *9 81
3 *8 24
2 *7 14
6 *6 36
9 *5 45
8 *4 32
1 *3 3
8 *2 16
3 *1 3

Third, add all of the products together!

10+81+24+14+36+45+32+3+16+3 =


Finally, divide the number by 11, and if the number divides evenly by 11, (meaning there is no remainder) then it is valid!

264/11 =


(This isn’t the only way to check for validity with an ISBN-10 number, but it is a quick way to identify the validity of the book!)

Now that you know how to identify the validity of a book, you can now buy a book knowing how to identify it and how to make sure it is valid!