Final answer:
The Luhn algorithm is used to calculate the check digit for a credit card number; the check digit for the given credit card number is 5, making the full number 4567 2654 6709 3325.
Step-by-step explanation:
The student is asking about how to find the check digit for a credit card number using a widely accepted algorithm called the Luhn algorithm, which is used to validate a variety of identification numbers. The credit card number the student has provided is 4567 2654 6709 332d, where 'd' represents the check digit that is to be calculated.
Step-by-step process to find the check digit:
- Starting with the digit farthest to the right, which is the check digit, and moving left, double the value of every second digit. If the result of this doubling is greater than 9, then add the digits of the result.
- Sum all the digits.
- If the total obtained in step 2 is a multiple of 10, the number is valid and the check digit is 0. If not, subtract the last digit of the sum from 10, and the result is the check digit.
Applying the Luhn algorithm to the given number:
Double every second digit from the right (excluding 'd'): 8, 5, 6, 7, 1, 12, 12, 0, 14, 3, 4, 6. Now sum the separate digits of the products greater than 9: 8, 5, 6, 7, 1, 3 (1+2=3), 3 (1+2=3), 0, 5 (1+4=5), 3, 4, 6.Add all numbers, including the unchanged digits: 8+5+6+7+2+1+3+3+6+0+5+3+2+0+9+3+4+6+4+7 = 85. Since 85 is not a multiple of 10, subtract the last digit of this sum (5) from 10 to find the check digit. Therefore, the check digit, 'd', is 10 - 5 = 5. Therefore, the complete valid credit card number is 4567 2654 6709 3325.