The island is also a major source of another essential and often invisible component of everyday objects: screws. And most go to the United States, where they are used to build airports, backyard decks and bathroom cabinets. For the United States, Taiwan has been the No. 1 source of screws and metal fasteners like nuts and bolts for more than three decades, with China gaining ground as the second largest. Taiwan’s screw factories, in the island’s south, sprawl across industrial districts like Lujhu and Gangshan, where the sounds of chugging machinery echo around the clock.