It is possible to run Artifactory on port 80, but it requires that the user that runs Artifactory has special permissions to do so.
This is because all ports under the number 1024 are considered to be 'privileged'.
As a "best practice", we suggest that you run a reverse proxy that will listen on port 80 and redirect the requests to Artifactory's port. (The default port is 8081 in the stand-alone version.) You can read about how to set this up here.
Although we highly discourage it, it is possible to change the listening port of Artifactory to listen on port 80 by making sure that the user that runs Artifactory has "admin" permissions and modifying the 'server.xml' file that is situated at: '$ARTIFACTORY_HOME/tomcat/conf/server.xml'.