Welcome to the community, Ginger_1!
Can you please provide us with more details about the external hard drive? Did you have the drive attached to your Mac while doing the factory restore?
I'd also recommend you to go to Disk Utility in Mac OS and check if the external hard drive is recognized there. You can also troubleshoot and detect if there are any issues with it. You can refer to
THIS ARTICLE from our knowledge base that will shed some light on the step-by-steps.
Keep me posted & Good luck!
SuperSoph_WD