Answer:
The check digit for the credit card number 532685030124460___ should be 9. This is determined by the Luhn algorithm, which is commonly used to validate credit card numbers.
Explanation:
The Luhn algorithm, also known as the modulus 10 or mod 10 algorithm, is a simple checksum formula used to validate a variety of identification numbers, such as credit card numbers, IMEI numbers, Canadian Social Insurance Numbers, and Greek tax identification numbers. It was created by IBM scientist Hans Peter Luhn and described in U.S. Patent No. 2,950,048, filed on January 6, 1954, and granted on August 23, 1960.
The algorithm is in the public domain and is in wide use today. It is specified in ISO/IEC 7812-1. It is not intended to be a cryptographically secure hash function; it was designed to protect against accidental errors, not malicious attacks. Most credit cards and many government identification numbers use the algorithm as a simple method of distinguishing valid numbers from mistyped or otherwise incorrect numbers.
The formula verifies a number by calculating a single digit that serves as the checksum.
Here's a step-by-step explanation of the Luhn algorithm:
Starting from the rightmost digit (the check digit), move left and double the value of every second digit.
If a resulting double digit is greater than 9 (e.g., 7 × 2 = 14), sum the digits (e.g., 1 + 4 = 5).
Replace the doubled digits with the resulting sum.
Add all the digits together (including the check digit).
The check digit is the rightmost digit of the sum of the digits modulo 10 (i.e., the remainder when the sum is divided by 10).
In the case of the given credit card number 532685030124460___:
Double every second digit, starting from the rightmost digit: 0, 0, 8, 1, 6, 2, 2, 6, 4, 5, 3, 2, 6.
Sum all the digits: 0 + 0 + 8 + 1 + 6 + 2 + 2 + 6 + 4 + 5 + 3 + 2 + 6 = 45.
The check digit is the rightmost digit of the sum of the digits modulo 10, which is 5.
So, the check digit for the given credit card number is 5, and the complete credit card number would be 5326850301244605.