I reckon, it has a lot to do if we are talking about a fan engine or a pure turbojet engine. As mentioned, the fan of a high bypass fan engine produces most of the thrust at take off/low altitude. That ratio reverses somewhat at high altitude where the core produces relatively more thrust than the fan.
Looking at a pure twin spool turbojet like the Olympus, the compressor has 6 LP pressure stages, 8 HP stages and single stage HP and LP turbines. Quite a few LP stages when compared to modern fan engines.
On the side, technically, the rotating compressors add speed to the incoming air and the stators convert this speed to pressure.