Show that the credit card number
4306 0912 4887 1457 is valid/invalid.
Explain how you know.

Step 1a. For a card number with an even number of digits (e.g., Visa or MasterCard), double alternating digits starting with the first digit in the sequence.
Step 1b. For a card with an odd number of digits (e.g., American Express), double alternating digits starting with the second digit in the sequence.
Step 2. If the doubling resulted in a number with two digits, add them together to get a single digit number
Step 3. Now go back to the original credit number and replace the digits that you doubled with the new value — either the doubled value, or the doubled value with the digits added together — and add it all up.
Step 4. Check to see if the sum is evenly divisible by 10 (you can simply look to see whether or not it ends with a zero).
If the card number does not pass this check, then it is not a valid number. If, on the other hand, it does pass, then it may be a valid number with valid credit report.