Reapplying free Win 10 Upgrade after factory reset.

Yes, you can.

Note: How to verify if you downloaded or installed the Windows 10 Anniversary Update

Select the option Upgrade this PC now if you want to upgrade right away, of if you want to download a ISO image or create a bootable copy on a USB thumb drive, choose Create installation media for another PC then click Next

A new option has been added to the setup screen for users reinstalling Windows 10 on a previously installed and activated system. If your system has a Digital License attached to it, Windows 10 will automatically upgraded:

You can also perform a direct install.

Step 1: How to download official Windows 10 ISO files

Step 2: How to: Perform a clean install of Windows 10

When you upgraded from a previous version of Windows or receive a new computer preinstalled with Windows 10, what happened is the hardware (your PC) will get a digital entitlement, where a unique signature of the computer will be stored on Microsoft Activation Servers. The Windows 7 or Windows 8 genuine license you were previously running will be exchanged for a diagnostics key.

Anytime you need to reinstall Windows 10 on that machine, just proceed to reinstall Windows 10. It will automatically reactivate. You will prompted to enter a product key a couple times through the installation, click I don't have a key and Do this later.

There is no need to know or get a new key, but if you have issues with Digital Licensing or the Activation Troubleshooter, you can utilize an existing Windows 7 or Windows 8/8.1 product key you already ownto reactivate if necessary. or use the reset function in Windows 10.

Download the Media Creation Tool and upgrade.  If you had upgraded to Windows 10 before your computer is activated and you do not need a key.  Just go to the bottom of the screen when asked for a key and click on Skip, Do this later, or I do not have one.

Media Creation Tool US;  Read the instructions.
https://www.microsoft.com/en-us/software-download/windows10