Is the word fábrica the same in Brazilian and European Portuguese?

Yes

The word "fábrica" is identical in meaning, spelling, and grammar in both Brazilian and Continental Portuguese. The only difference lies in pronunciation:

• Brazilian Portuguese: The vowels are more "open" and clearly articulated. Each syllable is pronounced with distinct, full vowel sounds.
• Continental Portuguese: The pronunciation is more "closed" or reduced. Unstressed vowels are often swallowed or shortened (for example, the final "a" is much more neutralized, sounding almost like a short "uh").

Brazilian Portuguese Examples

1. Eu trabalho em uma fábrica de sapatos. (I work in a shoe factory.)
2. A fábrica de doces é muito legal. (The candy factory is very cool.)
3. A gente vai visitar a fábrica amanhã. (We are going to visit the factory tomorrow.)
4. Essa fábrica está produzindo muito. (This factory is producing a lot.)
5. O dono da fábrica é meu tio. (The owner of the factory is my uncle.)

Continental Portuguese Examples

1. Eu trabalho numa fábrica de sapatos. (I work in a shoe factory.)
2. A fábrica de doces é muito fixe. (The candy factory is very cool.)
3. Nós vamos visitar a fábrica amanhã. (We are going to visit the factory tomorrow.)
4. Esta fábrica está a produzir muito. (This factory is producing a lot.)
5. O dono da fábrica é o meu tio. (The owner of the factory is my uncle.)