Every square number (except 1) is composite. Prime numbers only have two factors, one and the numbers themselves. Since square numbers also have at least the square roots as factors, they have to be composite.
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The square of any odd number is also an odd number for reasons that should be obvious.
Greater than one, numbers are either composite or prime, never both.
Yes, of course. In fact the product of any two numbers is composite unless one of them is 1.
8, 9, 10
You can figure out the "composite numbers" from any table of primes - all the positive integers that are not prime numbers are composite (the number one should also be excluded). The first four composite numbers are:4, 6, 8, 9