If you're looking to not just confiirm the architecture of the server you're logged into but also to use this knowledge in shell scripts, you can use the arch command instead of uname.
Just type arch in the command line, like this:
greys@s5:~ $ arch x86_64
When I run this on one of my Raspberry Pi systems, I see a different output, because they are not x86 based processors:
greys@becky:~ $ arch armv7l