said by 8744675:An HP Pavilion has about 72 screws
You forgot the /sarcasm tag on that. The highest screw count I've personally worked with was about 30 and that was a "everything comes out" situation. HP, Sony, IBM/Lenovo tend to be the worst though in general. The biggest issue for most people is not the quantity of screws but the variance of screws. I'd rather deal with 30 screws of 3 different sizes vs 15 screws of 8 sizes. I like to grab a sheet of paper and make a (very amateur) diagram of the system. As each screw comes out it goes on the paper diagram right near where it was removed. Works for me pretty well.
Rest of the advice is spot on.