Screen Freeze and Unresponsiveness - Factory reset didn't work


My daughter has a blue HTC One that was purchased in September.  After the recent KitKat update, her screen appears to freeze and appears to be unresponsive.  In actuality, if we lock the phone to turn off the screen and then turn it back on and unlock the screen, we end up having already navigated to where we expected to end up.  As you can expect, this is rather maddening.  This was not the behavior immediately before the update.  We executed a factory update, but it had no beneficial effect on the device.  Please advise.