If you wish to move Artifactory to the root of your website rather than using '/artifactory' there are several ways to accomplish this, one of which is described here. You can also change Tomcat's configuration files to accomplish the same thing.
Regardless of how you accomplish it, this will result in problems each time that you upgrade Artifactory because every new release of Artifactory is going to assume that the configuration has NOT been modified. The new/upgraded version of Artifactory will look for content in the '/artifactory' path, and won't find it there. To avoid this, you will want to remove the static '$TOMCAT_HOME/webapps/ROOT/index.html' file. This file redirects to '/artifactory' and will cause a failure if/when Artifactory is not found in that location.