I think the factory you were sent was definitely dependent on where the family lived. The community of Pesterzsebet, which is now District XX of Budapest, was taken to the Óbuda Brick Factory. Included in this round up were my mother, my aunt, and all my grandparents. They arrived in Auschwitz on 1 Jul 1944.

Here is more information about the various brick factories used in Jewish Budapest: Monuments, Rites, History By Kinga Frojimovics found on Google Books:

https://books.google.com/books?id=-wUg6rlWS2kC&lpg=PA391&ots=_rsYpnWwoS&dq=Obuda%20brick%20factory&pg=PA391#v=onepage&q=Obuda%20brick%20factory&f=false

Judi Gyori Missel