Something has been bothering me for quite a while and it seems only logical to reach out to the community and see if anyone else has any conclusions. 
Two things were repeatedly stated in TNG: The Galaxy-class was designed to hold families and civilian components of the crew, and the crew complement of the Enterprise was somewhere between 1012 and 1014. My question becomes this:
How many people on board the Enterprise were Starfleet personnel? Or, put another way, how many Starfleet personnel did it actually take to operate a Galaxy-class starship like the Enterprise?
I've scoured canon and non-canon resources like the TNG Tech Manual and Memory Alpha, but not a one of them has a good answer.
Thoughts?

Two things were repeatedly stated in TNG: The Galaxy-class was designed to hold families and civilian components of the crew, and the crew complement of the Enterprise was somewhere between 1012 and 1014. My question becomes this:
How many people on board the Enterprise were Starfleet personnel? Or, put another way, how many Starfleet personnel did it actually take to operate a Galaxy-class starship like the Enterprise?
I've scoured canon and non-canon resources like the TNG Tech Manual and Memory Alpha, but not a one of them has a good answer.
Thoughts?