If there is no phone number on the invitation to respond to and the invitation says "The favor of a reply is requested" does that mean you have to hand write a response?

Blueeyes

I would think this depends on the formality of the invitation, as well as your relationship to the person issuing you the invite. If a close friend, call and ask. If not, reply with either the enclosed response card or a short handwritten note.

Normally on a formal invitation, a written resonse if proper

Not necessarily. They could be assuming that you know the number or could have inadvertently forgotten to include it.

You can send an invitation cards thanking the person to invite you and also give the reply in that.