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Suppose you have a number n which is not a square.

Suppose now that a is a factor of n ie there is some integer b, such that a*b = n. Now since n is not a square, b is not the same as a. Thus for every factor a, there is another factor b ie the factors come in pairs. Therefore, there are an even number of factors.

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Q: Why do all numbers that aren't square numbers have an even number of factors?
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