In Linux, you can check your distribution with the uname command:
The output will read x86_64 for 64-bit and i686 or similar i386 for 32-bit.
The packages are built (optimized) for the:
i386 - Intel 386 processor
i486 - Intel 486 processor
i586 - Intel Pentium early AMD
i686 - Intel Pentium Pro and beyond
Compilations are backwardly compatible (i686 will run progs for i386) but not forwardly compatible.
I hope you will get your answer.