To find out on what partition is a file located, use the df command.
Syntax: df path/to/file
$ df /etc/passwd
Filesystem 1K-blocks Used Available Use% Mounted on
/dev/sda1 19609276 3227140 15386040 18% /
To filter the text, in order to get only the partition name, use this command:
$ df /etc/passwd | tail -1 | cut -d' ' -f 1
/dev/sda1