The phrase "a factory which is" is correct and usable in written English.
It can be used to introduce a clause that provides additional information about the factory being discussed.
Example: "We visited a factory which is known for its innovative production techniques."
Alternatives: "a factory that is" or "a factory which has".
Ms. Bawa set up a factory, which is run by her sister, in New Delhi; she makes frequent trips there to develop new patterns and products.
Because we'd noticed that on the previous film, which was not a heavy film, we had felt like the shopfloor manager in a factory, which is still a respectable job, but not what we wanted to do.
There, Mitra finds work at a factory which is, coincidentally, owned by Mardjohan.
"So I went all factory, which is an even bigger headache".
In that sense, it's sort of a 'startup factory' which is a product of a startup factory itself, German-syle, of course.
"In the war she joined the WAAF [Women's Auxiliary Air Force] but ran off and as punishment the authorities sent her to work in a munitions factory, which is how she ended up in this part of the world.
Today, the ease with which the chef discusses the ins and outs of pasta production makes him sound like the foreman of a small factory, which is not far off the mark: many days some 25 pounds of dough run through the machines to create the many varieties of pasta on the menu.
I was the night foreman of a galvanizing factory, which is hot and smelly and dirty and miserable.
The oldest Bake Off contestant to date used to work in a sausage factory, which is where she met her late husband Richard.
"They let me into a cigar factory, which is fascinating.
Yield forecasting is a very important task to a semiconductor manufacturing factory which is a typical group-decision-making environment.
