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You shouldn’t need to know the ports to be able to update, unless of course you are tightening your firewall rules, etc.

However the avast update uses port 80, see image of my firewall log and you will see avast.setup connecting to the downloadxxx.avast.com where xxx is one of the download servers outbound TCP, remote port HTTP (80).

You will see the logs for DNS but that is to get the IP address for the downloadxxx.avast.com domain and is normal for all connections.

I suspect that you may not be asking for this though, rather the IP addresses and that it an entirely different ball game.