How to Verify an ISBN

ISBN is abbreviation of International Standard Book Number, which usually can be found on the back of a book. 

This instructable is designed to help people find out whether a ISBN is valid using easy mathematics.

You will only need a pen/pencil, a piece of paper. 

Step 1:

Find out what kind of ISBN you have.

Two kinds of ISBN is now used for a book, 10 or 13 digits.

Usually, a 13 digits ISBN is converted from a 10 digits one by adding a "978" prefix and alter the last digit, which is often called the check digit.

Step 2-4 for 10 digits ISBN.
Step 5-7 for 13 digits ISBN.

Step 2:

In case you have a 10 digits ISBN, for example, the ISBN for the book Gravitation . 
0-7167-0344-0
You need to assign the position of each number from left to right.

Step 3:

Multiply each number by its position number and then sum up the products.

Step 4:

Divide the sum by 11 and find out what is the remainder. 
If the remainder is zero, then it is a valid 10 digit ISBN.
If the remainder is not zero, then it is not a valid 10 digit ISBN.

Step 5:

If you have a 13 digits ISBN. 
978-0-7167-0344-0
Also assign the position of each number from right to left

Step 6:

Multiply each number by an alternating 1 and 3 and then sum up the products.
Odd number positions by 1.
Even number positions by 3.

Step 7:

Divide the sum by 10 and find out what is the remainder.
If the remainder is zero, then it is a valid 13 digit ISBN.
If the remainder is not zero, then it is not a valid 13 digit ISBN.