How to reinstall macOS without factory disk

Because the factory media (CD or DVD, etc) is evidence of possession

of License to use the system; grey label mac-specific installer, or Retail

mac system installer discs, would be proper proof for legal use.

On the other hand, if you have a 'multiple install' factory set of discs;

there may be only one set of those, for several separate Mac systems.

Business, schools, and institutions had use of those versions.

When I happen to find a good set of Mac OS/OS X installer discs at

yard sale or in secondhand store bin, almost always bought them..

A few are rare enough now, to have interest over 200%, if re-sold.

However for personal use, to not expose original system install-restore

disc media to wear or damage, I may have and use in-house, full clones.

These on external drives, in partitions, can be useful to repair, restore,

and rebuild Macs. Not all enclosures can be used as startup volume;

often the external hard drive needs self-powered AC source, w/ "oxford

-type" chipset, a circuit within enclosure. For PPC macs, & correct format.

Bench testing vintage hardware to restore function, as hobby or avocation,

begs one to improvise. If you need to, go full-retro & save old Mac via clone.

So you could a Clone for test purposes; to troubleshoot, repair, restore and

not necessarily use the 'original media' per each endeavor. An OEM disc or

floppy may be proof enough, of intent to keep in step with original license.

(This idea also absolves the need to download duplicate backups for newer

mac where systems are downloaded and then install; restoration from clone

is fast and practical; another means of backups beyond Time Machine.)

By seeking and saving old system install media, a hobbyist can include proper

system installer with repaired/restored old vintage obsolete hardware. As I did.

You cannot.