First of all, a modified version of your service. 
a )
var app = angular.module('app',[]);
app.factory('ExampleService',function(){
    return {
        f1 : function(world){
            return 'Hello' + world;
        }
    };
});
This returns an object, nothing to new here.
Now the way to get this from the console is 
b )
var $inj = angular.injector(['app']);
var serv = $inj.get('ExampleService');
serv.f1("World");
c )
One of the things you were doing there earlier was to assume that the app.factory returns you the function itself or a new'ed version of it. Which is not the case. In order to get a constructor you would either have to do 
app.factory('ExampleService',function(){
        return function(){
            this.f1 = function(world){
                return 'Hello' + world;
            }
        };
    });
This returns an ExampleService constructor which you will next have to do a 'new' on.
Or alternatively,
app.service('ExampleService',function(){
            this.f1 = function(world){
                return 'Hello' + world;
            };
    });
This returns new ExampleService() on injection.