Zoom factor is term that is very often wrongly interpreted and causes misunderstandings with persons that are not familiar with photography terminology. When we take 2 objectives and for first say it has 5x zoom and for the other that it has 8x zoom, many will think that the other one will give more zoom i.e. more narrow field of view angle. However these 5x and 8x is completly irrelevant if we don't have the most important information, and that is objective's focal point lenghts range. So first objective can have range 100-500mm and that is 5x zoom, and the other one can have 30-240mm and that is 8x zoom. So, zoom factor doesn't determine power of objective, but it is just simple display of relationship between start and end focal point lenght of some objective.
Graphical explanation of zoom factor relationship