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

More-or-less the same way that you do. In school, you memorized single-digit addition, multiplication, subtraction, and division. Then, you learned how to do multiple-digit problems as a sequence of single-digit problems.

If you wanted to, you could multiply two twenty-digit numbers together using nothing more than knowledge of a simple algorithm, and the single-digit times tables.