meaning of 'zu Viert mehr Platz' in a sentence

Question

In this sentense,

Zuerst wollten wir nur eine größere Wohnung, um zu Viert mehr Platz zu haben.

I would interpret it as

First, we just wanted a bigger apartment in order to have a fourth room.

But google translator interpreted it as

First, we just wanted a bigger apartment in order to have four more rooms.

I thought because it's "Viert mehr Platz", it's "fourth added space".
If it were "four more rooms" it would have been "vier mehr Plätze".
Who is correct? me or google translator?
(I'm studying on my own, and sometimes have this kinds of questions..)

Answer 1

Both your interpretation and the Google translator are wrong in this case. Zu Viert describes that the sentence is about a bunch of four people.

The phrase can be extended to other numerals larger or equal than 2:

Zu Zweit, zu Dritt, zu Viert, zu Fünft, zu Sechst, ..., zu Achzigst, ...

Other examples:

Wir sind zu Viert verreist
We travelled as a group of four people

Heute waren wir nur zu dritt
Today we were only three

Answer 2

None of your translations is very accurate, unfortunately. (Google:Chan Kim 0:0)

zu viert translates roughly to "the four of us".

So the translation would be along the line of

First, we just wanted a bigger apartment to have more room for the four of us.

First, we just wanted a bigger apartment to have more room for our [group|family] of four

So, nothing is said about the apartment, but rather the amount of people who want to live in there.