Some more on Formats.
First, Dextermat was right to indicate this has NOTHING to do with "Low-level Format". That procedure is done at the HDD factory. It is very specific to the hardware of the disk device, and it actually creates the magnetic tracks and their boundary markers on the blank media platters, plus establishes a whole bunch of hidden data and resources necessary for the hard drive's own control board to manage its many functions.
What many these days call "Low-level Format" actually means a two-step process necessary on any new empty disk (also can be re-done on used disks) before it can be used by an Operating System. The first is Partition. This writes to specific standard locations at the very start of the disk an MBR (a small machine code piece used to boot from the disk) and the Partition Table, a set of data detailing exactly how the space on this physical device is allocated to one or more Partitions. From then on, each Partition is treated as a separate "drive". The second step (and this one really is done by the OS since its details depend on what OS is using the disk) is Format, done separately for EACH "disk" or Partition. It writes the hidden key data structures at the beginning of the disk used to track the use of disk sectors to files. These include a Root Directory, a table of use of Allocation Units, and some other files I don't understand!
Now, a Quick Format will do that second step - write the key structures - and use the Partition size to tell you the available space and a few other things, but it does NOT look at the rest of the disk. A Full Format, on the other hand, does a complete test of every individual sector of that drive by writing material to it, then reading it back and checking that it is right. Recent versions of Windows conclude this part by writing zeroes specifically to the sectors when they are done. If Windows finds any sectors unreliable, it marks them in the Allocation Unit tracking files so they are never used. Because this is a lot more work, a Full Format takes much longer. We did that recently on a 1.5 TB drive in a fast machine, and Full Format took over 5 hours, versus less than 10 minutes typically for the Quick version.
Most new drives are so reliable there are no faulty sectors for Windows Full Format to find, but it is not impossible. So a Full version is just an extra safety move if you have the time.