How long do I need to hold the pairing button on the K580 to initiate pairing?

You need to hold the channel/pairing button for 3 seconds to initiate the pairing process on the K580. This is shown as part of the step-by-step setup instructions in the manual. (Page 1)

From the official Logitech Logitech K580 Multi Device Wireless Keyboard Chrome OS User manual, page 1

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