Mac OS X's Time Machine backup utility won't work with FAT32.
It is recommended that you choose a Time Machine destination that’s roughly two-to-four times the size of the drive you are backing up.
FAT32 is an older file system that’s largely relegated to USB flash drives and other external drives.
Windows uses NTFS for its system drive, and it’s also ideal for other internal drives.
exFAT is a modern replacement for FAT32, and more devices support it than do NTFS — although it’s not as widespread as FAT32.
FAT32 file system.
This type of a file system has a built-in limitation on the size of the files that it may contain.
Although the total size of the files that you can copy to a FAT32 drive could be as large as 2TB (or the physical capacity of the drive, whichever is smaller), the size of each individual file may not exceed 4GB.