Update to Office 2016 for Mac v16.29.1 using Microsoft Autoupdate

You can get the full and current 16.17.17 installer directly from Microsoft:

https://docs.microsoft.com/en-us/officeupdates/release-notes-office-2016-mac

The top link, Office suite (all applications), contains the entire suite as a single download.

Or, if you meant Office 2019 (or 365), you can click on the Update history link at the left to download the current 16.32 for either.

Check with Microsoft for an update. The original versions of Office 2016 were 32-bit, but they have an update that makes it 64-bit.

I'm not sure if the updater is 32-bit, though.

Office 2016 should be 16.17.17. Not sure where you got your version.

If it was this then its not 2016 and may even be a fake

How did you do it?

My 2016 Office worked after I went (in Word)

Help, Check for updates.

Checked "Automatically keep Microsoft apps up to date"

It also updated the updater

Office v 16.16.17 (191208)