Q: I have just done a Mac restore back to factory setting and realise that I have lost Pages and Numbers. Can the system see that I have already bought them and I can download them for free or do I have to buy them again?

Apple only keeps the current release of Pages, Numbers, and Keynote in the App Store for redownload. The current Pages v6, Numbers v4, and Keynote v7 now require macOS Sierra installed before they can be downloaded. Your hardware would have to be compatible for a Sierra installation.

Your only shot will be to get your previous Pages, and Numbers off of the backup that you made before you wiped that Mac. If these were Pages '09, and Numbers '09 that were installed from the Apple iWork '09 DVD, then you will have to reinstall from that DVD, and then apply the Apple iWork 9.3 updater (only for iWork '09 DVD installed applications).

If you did a backup prior to your factory restore (why did you do that?) then you can use Applications/Utilities/Migration Assistant to restore everything/or only what you want from your backup.

If you simply want to install everything from scratch, just log into the App Store with your Apple ID and it should be available to install free.

Peter