rational and prime numbers
No, it is not.
The set of rational numbers includes the set of natural numbers but they are not the same. All natural numbers are rational, not all rational numbers are natural.
The Real numbers
It is the rational numbers.
rational and prime numbers
It belongs to the set of prime numbers
No, it is not.
All factors are whole numbers and all whole numbers are rational numbers (a rational number is one which can be expressed as one integer over another integer, and whole numbers can be expressed as themselves over 1), thus all factors are rational numbers and so all greatest common factors are rational numbers. The set of whole numbers is a [proper] subset of the set of rational numbers: ℤ ⊂ ℚ
The set of rational numbers includes the set of natural numbers but they are not the same. All natural numbers are rational, not all rational numbers are natural.
The integers. Also: the rational numbers, the real numbers and (depending on your definition) the complex numbers.
Yes - the set of integers is a subset of the set of rational numbers.
The Real numbers
The derived set of a set of rational numbers is the set of all limit points of the original set. In other words, it includes all real numbers that can be approached arbitrarily closely by elements of the set. Since the rational numbers are dense in the real numbers, the derived set of a set of rational numbers is the set of all real numbers.
Many infinite sets appear in mathematics: the set of counting numbers; the set of integers; the set of rational numbers; the set of irrational numbers; the set of real numbers; the set of complex numbers. Also, certain subsets of these, such as the set of square numbers, the set of prime numbers, and others.
It is the rational numbers.
No. A real number is only one number whereas the set of rational numbers has infinitely many numbers. However, the set of real numbers does contain the set of rational numbers.