We use the determiner "a" for countable nouns. For example: A tree A cat An apple A bus A person An organ We do not use it for uncountable nouns. For example: Milk Choas Furniture Sunshine Sleep Snow Water Some nouns can be used with and without a determiner such as the word "part". When this happens, it doesn't matter which one you go for because they mean the same thing. So you might hear someone say, "a part of the house" and you might hear another person say, "part of the house". They mean the same thing.

Both of them should be 'part of' 'a part of' is slightly different.. and hard to explain … If I think of a good example I'll tell you

Being "a part of" something means you are included in a group. "Part of" something means it is a fraction of the whole.