How does a website know if a certain creditcard number is wrong instantly

I was renewing my Internet subscription through the online portal of my ISP. What struck me was when I was entering my credit card details, I entered the type of my credit card (MasterCard, Visa, AA, etc), and when I entered the numbers, there was one number that I entered wrong. When I pressed the submit button, the website automatically gave me an error that the card number I entered was invalid. I sense this was done locally in the browser and no data was pushed and checked on a server and sent back a reply.

My question is, is there any sequence of numbers each vendor has? Otherwise, how would the website (locally) know about the wrong number ?