Why are people leaving out the indefinite article 'a' before seemingly random nouns? [closed]

In English, when you are talking about a place being attended as an institution, we often leave out the article; but the choice of which institutions you can do this with varies according to the variety of English.

So in British and American English we say to/in prison and to school (though there is another difference in the preposition: AmE in school, AmE/BrE at school). But British English says to/in hospital where American English says to/in the hospital (even if this is not in reference to a particular hospital).

It's not just geographical varieties either: there is a significant number of instances of at conference in the GloWbE corpus - more for UK and New Zealand than the US: these are predominantly in the world of politics and unions, and little used outside those fields.

Your example with "factory" is not idiomatic in any variety of English as far as I know, and I would suppose that it is either a mistake, or written by a non-native writer.