Could I write a HttpInterceptor as a service?

Question

I'm rather confused over the difference between a factory and a service and why one would choose one over the other. Here I have a factory but is it possible to write as a service and if so what would it look like? Also what's the advantage of using a service or a factory here?

app.factory('testInterceptor', ['$q', function ($q) {

    return {
        'request': function (config) {
            return config;
        },
        // optional method
        'requestError': function (rejection) {
            return $q.reject(rejection);
        },
        // optional method
        'response': function (response) {
            return response;
        },
        // optional method
        'responseError': function (rejection) {
            return $q.reject(rejection);
        }
    }
}]);

app.config(['$httpProvider', function ($httpProvider) {
    $httpProvider.interceptors.push('testInterceptor');
}])