Thanks for reaching out to us on HP Support Forums. 🙂 I came across your post and would like to help.
I understand that you have a new HP Notebook - 15-ay041wm and it does not connect via bluetooth to your HP Deskjet 4580 printer and to your Samsung G8 smartphone.
To provide an accurate resolution, I need a few more details:
Are you trying to communicate the laptop via bluetooth to the printer in order to print and scan?
Have you tried the bluetooth pairing between the laptop and the Samsung phone?
Meanwhile, I did some research and found that the HP Deskjet F4580 All-in-One Printer does not have the bluetooth functionality. However, the printer can either be connected directly via a USB cable to your laptop or it can be connected wirelessly to a wifi network so that it can print/scan from the laptop and also from the Samsung phone. You may view the detailed product specifications for your HP printer here.
You may refer to this HP document to pair your laptop via bluetooth with your Samsung phone.
Secondly, if you could let me know how you plan to connect your printer, I'll be happy to assist you further. Let me know how it goes.
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