How do programming languages handle huge number arithmetic

Question

For a computer working with a 64 bit processor, the largest number that it can handle would be 2⁶⁴ = 18,446,744,073,709,551,616. How does programming languages, say J

Answer 1

As a thought experiment, imagine the numbers stored as a string. With functions to add, multiply, etc these arbitrarily long numbers.

In reality these numbers are probably stored in a more space efficient manner.