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There is no highest number
There is no highest number, highest prime number, or highest composite number. Therefore, there can't be a second-highest, third-highest, etc., of any of these types of numbers, either.
There is an infinite number of possibilities to the highest number.
There is no highest square number. If there was such a number then that number squared would be a higher square number!
The highest factor of any number is the number itself.