Please correct me if I'm wrong, but in a high bypass turbofan engine, about 80% of the total thrust are generated by the fan, which is driven by the low pressure turbine. The low pressure compressor, sometimes also referred to as 'booster', is pre-compressing the air that enters the core engine before it is compressed further by the high pressure compressor. The HPC and HPT of a turboshaft engine are often referred to as "gas generator": The HPC compresses the inlet air which is mixed with fuel and then burned inside the combustion chamber. The combustion gas powers the gas generator or HP turbine, which in turn drives the HP compressor. The energy that's left in the combustion gas (which is, obviously, significantly greater than the energy required to power the HPC, because the fan does require a LOT of power, I'm just guessing but it could well be about 20,000 hp in a CFM56) then powers the so called power turbine, or in a two spool engine like the CFM56, the LP turbine which drives the fan. There will still be a little bit of energy left in the exhaust gas, which does add to the total thrust as it exits the tailpipe. Secondary functions of the HPC include driving accessory gearbox(es), supplying bleed air for various functions such as anti-ice, pressurisation etc.