The military CETME Models A, B, and C classify as battle rifles,
firing the full power 7.62x51 cartridge. The 5.56x45 CETME Model L
classifies as an assault rifle.
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$600 to $700
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Not without modification.
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There are full auto weapons capable of chambering the .308
Winchester, yes, although these were actually designed for the
dimensionally similar (but not identical) 7.62x51 cartridge. M14,
AR10, CETME, G3, FN FAL, just to name a few.