Please tell me which is the correct phrase below:
One of my favorite movies
or
One of my favorite movie
Please tell me which is the correct phrase below:
One of my favorite movies
or
One of my favorite movie
One of means you are talking about one item from a group.
If there is one apple on the table, and I want you to take that apple, I would not say
*Take one of the one apple on that table.
but
Take the apple from that table.
If there are more apples, I can tell you
Take one of the apples on that table.
To talk about one of when there is only one is not a very common thing. So when you say :
It is one of my favourite movies.
You are talking about a single movie that is somewhere in your list of favourites.
If you only have one single favourite movie, you say:
It is my favourite movie.
Saying
*It is one of my favourite movie.
Would mean you are talking about one movie from the one favourite movie you have. Although I guess you could construct a context where that makes sense, I am quite sure that in most cases you will only confuse people. :)
As Jay remarks correctly in his comment, if you do not know whether there is one object or more, you can still use one of X, but X is still plural. So if I tell you "take one of the bikes from the shed if there are any", it is of course possible there is only one bike, and that does not mean you should come back to me and berate my grammar... If I know there is exactly one bike in the shed, I would say "take the bike from the shed".

So "One of my favorite movies" is correct. It is like saying "One of the balls" (i.e. one of the many 'balls') (not ball)
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You're probably confusing the following two expressions
1) A/one favourite movie of mine
with
2) One of my favourite movies
The construct of No1 is: A/one + singular noun + of mine
E.g., A friend of mine OR one friend of mine; a book of mine OR one book of mine; an aunt of mine OR one aunt of mine, etc. The indeterminate article, a, is usually preferred because "a" tells us that the thing referred to is nonspecific. "A" is also used for introducing a thing in the topic of conversation for the first time.
In the following construction one + of the/these/my + plural noun the noun is in plural because the adjective one is telling us the number of things from a group. Thus we have: