Real Power Output may not be equal to Apparent Power Output. You
can view real power as the useful power that came out and apparent
power as the power that should be observed.
This is because in real life, nothing is perfect, whereas in
physics, most calculations assume perfect conductors, perfect this
perfect that...
The power loss can come from internal impedance, parasitic
capacitance or inductance. Some power are also imaginary; power can
be calculated in terms of complex numbers.
In view of the above information, you can also summarize that real
power <= apparent power.
Hence, because power factor is real power / apparent power,
power factor <= 1