We would usually say "I won first prize".
If you say "I won the first prize" it sounds like you won some prize that came up first, whatever that was. The term "first prize" indicates that you were the winner of a competition. The actual prize isn't really the focus.
2020年6月18日
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Thank you, Nay.
2020年6月19日
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Thank you, Elizabeth.
2020年6月19日
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Either actually are ok honestly. If you are responding to a question, it would be more likely to be the first one I think, but they are both correct. You'd be more likely to say the 2nd though!
2020年6月18日
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I was awarded first prize in the competition. Or I won first place in the competition .