You could start counting.
And before long you'll have to decide to what degree you want to break it down. A mag catch is two pieces and a trigger guard is four, but most of us get those as one piece.
A quick count gets me 22 pieces for a barrel assembly:
barrel
barrel extension
barrel indexing pin
flash hider
crush washer
FSB
FSP
FSP detent
FSP detent spring
FSB taper pin
FSB taper pin
sling swivel
sling swivel rivet
barrel nut
delta ring
weld spring
snap ring
handguard half
handguard half
handguard endcap
gas tube
gas tube roll pin
Somebody will probably be along to tell me what I forgot. Anyway, that's all the fun I'm going to have with it.
ETA - Above is for the A2 and doesn't count the pieces included in a side sling swivel mounting.
EATA - And I forgot to break down the handguards and heat shields - I'm done.