A positive integer is an integer to the right of zero on the number line. It is more then zero
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An integer that divides into another integer exactly is called a Factor.
Yes, by definition.
If you divide an integer by another integer, the result is a rational number by definition.
No. by definition, the polynomial should contain an integer as exponent and square root 1/2 is not an integer.
Prime means that the integer can only be divided by itself and 1.