When i Try to connect to public games it gives me the login screen and and when i log in it says: Insufficient membership. Login requires a membership which owns the game. Please buy the game on our website or via retailers (Steam, GOG). Even though i bought the game on GOG. Can someone Please help me?

Go to your account, click on Factorio & select 'serial keys' from the 'more' menu. Use this on the factorio website to upgrade your account there (You may need to make one). Then login with your Factorio account in game and it should work.

Hi，I meet the same problem.But I can't find the key in my gog software.
Thanks.

Its not in GOG Galaxy, its on the website.

Thank you:D
I found the key on the GOG website.
But my account on the Factorio website can't upgrade the membership.Upgrade didn't work.
The price of Factorio on the GOG is expensive than Steam version in my country,but the service is.......horrible
sigh... Hi,mine is the same situation.But upgrade can't work

Thanks for helping.
when I click Upgrade,there is no any action just as i haven't click it.
No entering code screen,click and just the same page.

Strange, perhaps you need to disable any ad-blockers (If you have one) or try a different browser?

Thanks for reply.
My chrome haven't any add-ons.Change to Windows' original explorer, doesn't work too.
:C