For example I have a factorial program that needs to save really huge integers that can be 50+ digits long. The absolute maximum primitive data type in C++ is unsigned long long int
with a maximum value 18446744073709551615
which is only 20 digits long. Here's the link to the limits of C++: http://www.cplusplus.com/reference/climits/
How do I store numbers that are larger than that in a variable of some sort?
If you already have a boost dependency (which many people these days do), you can use the boost multi-precision library. In fact, it already has an example of a factorial program that can support output up to 128 bits, though extending it further is pretty trivial.