Luhn Algorithm for Credit Card Validation 🔍🧮

Overview

The Luhn algorithm, also known as the modulus 10 or mod 10 algorithm, is a simple checksum formula used to validate various identification numbers, most notably credit card numbers. This project implements the Luhn algorithm to validate credit card numbers and provides a detailed explanation of how the algorithm works.

How the Luhn Algorithm Works

The Luhn algorithm checks whether a given credit card number is valid by performing the following steps:

1. Reverse the Credit Card Number:

   • Start with the rightmost digit (check digit) and move left.

2. Double Every Second Digit:

   • Beginning with the first digit on the right, double the value of every second digit.
   • If doubling a digit results in a two-digit number (e.g., 7 × 2 = 14), add the digits of the product together (e.g., 1 + 4 = 5).

3. Sum All Digits:

   • Add all the single digits obtained from the above step to the digits that were not doubled.

4. Check the Total:

   • If the total modulo 10 equals 0, the credit card number is valid; otherwise, it is invalid.

Example

For the credit card number 4539 1488 0343 6467:

1. Reverse: 7 6 4 6 3 4 3 0 8 8 4 9 3 5 4.
2. Double every second digit: 7, (6×2=12), 4, (6×2=12), 3, (4×2=8), 3, (0×2=0), 8, (8×2=16), 4, (9×2=18), 3, (5×2=10), 4
3. Replace double-digit results with their digit sums: 7, 3, 4, 3, 3, 8, 3, 0, 8, 7, 4, 9, 3, 1, 4
4. Sum all digits: 7 + 3 + 4 + 3 + 3 + 8 + 3 + 0 + 8 + 7 + 4 + 9 + 3 + 1 + 4 = 69
5. Check total:

• 69 % 10 = 9 (Invalid card number).

Resources

• Luhn Algorithm - Wikipedia
• Credit Card Validation Rules