Can I use my xbox controller on another xbox?

I just got minecraft for xbox 360 today but my xbox isn't connected anymore since I used the cable from the xbox and put it in a karaoke machine. My friend has an xbox 360 and I thought maybe I can bring my minecraft over her house and play WITH her so can I use my xbox controller to play with her and her xbox controller? I know how to do split screen already but all I'm asking is that is there any way my xbox controller and her xbox controller will work on her xbox? I think it will work but I got my controller along with my xbox so i think I can't change it but if there's anyways can change it and change it back to my xbox after I get the cables back together again I would really appreciate it.

All you have to do is pair the controller with her Xbox, and then it will work on her Xbox.

Then you pair it back to your Xbox when you're done.

If you don't know how to pair an Xbox controller to an Xbox, then I don't know how you own an Xbox.

Yes. All you have to do is pair the controller with your friend's Xbox. Then, when you're ready to use your Xbox again you pair it with yours.

To pair your controller to the Xbox, first you must power on the Xbox and your controller. Then press they sync button on the Xbox 360. (The sync button is a small round button near the Power button on the Kinect-ready Xbox 360, and next to the memory card deck on the original Xbox 360.) Next press and hold the sync button on your controller until the correct light around the Power Button indicates a connection to the Xbox 360. To pair with your Xbox again, simply repeat the steps using your unit.