You can set the limits for the groups instead of users to globally change the limits for all the users at once.
You also need to ensure that pam_limits is configured in the /etc/pam.d/system-auth file, or in /etc/pam.d/sshd for ssh, /etc/pam.d/su for su, or /etc/pam.d/login for local logins and telnet if you don't want to enable it for all login methods. Here are the two session entries which you need to have in /etc/pam.d/system-auth file:
session required /lib/security/$ISA/pam_limits.so
session required /lib/security/$ISA/pam_unix.so
Now login to the user account since the changes will become effective for new login sessions only. Note that the ulimit options are different for other shells.
To make the above changes permanent, you could also set the soft limit equal to the hard limit in /etc/security/limits.conf which I prefer:
user/groupname soft nofile 63536
user/groupname hard nofile 63536
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