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

Think of one machine-size number as a digit and apply the algorithm for multi-digit multiplication from primary school. Then you don't need to keep the whole numbers in registers, just the digits as they are worked on.