Nope, "its" doesn't use an apostrophe because then it would be the same word as the contraction. Also it's a pronoun when used that way and you don't say "her's" you say hers. Hard to explain. But all those little grammatical things bother me, mainly when I see them in web pages, newspapers, published things, etc. I mess up too sometimes if I'm out of it and type something hastily.
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