You have two options. Either you can use one of the existing libraries that handle types this large, or you can handle it yourself.
I usually point people towards the GNU Bignum library, but others exist.
If you decide to handle it yourself, there are many options. For example, you could store the value as a string, and define your own operations (+, -, /, *) for working on those values. Alternatively, you could make each of these big values a linked list in which each node in the list holds one of the digits, and again implement your own basic operations. There are many ways to do it.
If you're using Bloodshed Dev C++, please don't. It's an awful choice and you're doing yourself no favours.
If you want to use an IDE, there are a number of choices. In no particular order, off the top of my head:
Orwell's updated Dev C++
Whatever version of Visual Studio is free at the moment from Microsoft
Alternatively, I always like to recommend beginners at least learn how to use their compiler by hand, in which case you need no more a modern compiler (Clang/LLVM or the GCC are good choices), a text editor, and a couple of build tools such as Make.
I am working creating a fully encapsulated, homogeneous singly linked data structure. The Listing class and SinglyLinkedList class that are part of the whole application compile fine, but the problem ...