As of SharePoint 2010 it’s really simple to change the port number of Central Administration.

When installing the stand-alone version of SharePoint (which generates a portnumber) or simply if you want to change it (maybe some other software wants to use that port)

The simplest way to accomplish this is by using a powershell command.

Type : Set-SPCentralAdministration -Port <your preferred portnumber>

It will change the portnumber on the fly.

BUT…… Keep the following in mind when changing the portnumber.
The moment a webapplication is created, a directory is created based on the original portnumber. When you change the portnumber, the name of the dorectory will NOT be changed and still refelct the original portnumber.

Directory: C:inetpubwwwrootwssVirtualDirectories<original portnumber>

If the names of these directories don’t match your expectations, always take a look at the configuration in IIS.
In IIS you can see both the directory and portnumber and you might see that someone changed the portnumber.