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

There are lots of specialized techniques for doing calculations on numbers larger than the register size. Some of them are outlined in this wikipedia article on arbitrary precision arithmetic

Low level languages, like C and C++, leave large number calculations to the library of your choice. One notable one is the GNU Multi-Precision library. High level languages like Python, and others, integrate this into the core of the language, so normal numbers and very large numbers are identical to the programmer.