What factors into it most is what type of cow it is. Some types have been bred over the years to be smaller in size and those produce less milk (they also eat less which is one reason why they are popular). Others are bred to produce the maximum amount of milk possible, and they tend to be super large like Holsteins which will produce milk just shy of a year after giving birth. It equals up to thousands of gallons a year. It's a lot for a family.
Ah, just saw RichZ answered too. He's a good one with lots of knowledge.