Q. How many balls of string does it take to reach to the moon?
A. One - if it's long enough.
The number of discs it will take depends on what size the discs are and how much stuff you need to put on them. Why don't you set up a backup job and let it estimate the total size, then come back with that figure.
My Computer
Computer Manufacturer/Model Number
Self
OS
Main - Windows 7 Pro SP1 64-Bit; 2nd - Windows Server 2008 R2
CPU
Main - Core i7 2600K; 2nd - Core i7 920
Motherboard
Main - Asus P8Z68-V Pro/Gen3; 2nd - Gigabyte GA-EX58-UDR3
Memory
Main - 16GB Corsair Vengeance; 2nd - 12GB Corsair Vengeance