Final answer:
To verify the validity of given credit card numbers, one must use the Luhn algorithm, which involves doubling every second digit from the right, correcting for double-digit products, adding together all digits, and checking if the total is a multiple of 10.
Step-by-step explanation:
To determine whether given credit card numbers are valid, we can use the Luhn algorithm, a simple checksum formula used to validate a variety of identification numbers, most notably credit card numbers. Here's a step-by-step explanation on how to use the Luhn algorithm:
- Starting with the second to last digit and moving left, double the value of every second digit. If the product of this doubling is greater than 9, then sum the digits of the products (e.g., 16: 1 + 6 = 7).
- Add together doubled digits with the undoubled digits from the original number.
- If the total sum obtained in step 2 is a multiple of 10 (i.e., the sum ends in 0), the number is valid according to the Luhn algorithm; otherwise, it is invalid.
Since the validity check has to be performed for each number individually and the numbers are not provided in full here, the student will need to apply these steps to each credit card number to verify its validity.