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

Most languages store them as array of integers. If you add/subtract two to of these big numbers the library adds/subtracts all integer elements in the array separately and handles the carries/borrows. It's like manual addition/subtraction in school because this is how it works internally.

Some languages use real text strings instead of integer arrays which is less efficient but simpler to transform into text representation.