Question

The number 23 is:
A) A prime number
B) A real number
C) An irrational number
D) A rational number

A) A, B, D are correct
B) A, B, C are correct
C) B, C, D are correct
D) A, C, D are correct

Answer 1

Hint: Every whole number is a rational number and every rational number is a real number. First, we will find out whether 23 is a prime number or not by the prime factorization method. Then we will find out whether 23 is a rational or irrational number by the definition of the rational number. Moreover, either rational or irrational, it will be a real number.

Complete step by step solution: A prime number can be defined as a natural number whose factors include 1 and the number itself only. It means no other number can be a factor of a prime number.
We have: the number 23
We can surely say that the number 23 is a whole number.
Prime factorization of a whole number can be defined as writing the whole number in the product of its prime factors.
Prime factorization of 23 is:
$23 = 1 \times 23$
So, factors of 23 include 23 and 1 only.
Thus, by the definition of Prime numbers, we can conclude that 23 is a prime number.
So statement A is correct.
A rational number can be defined as a number which can be expressed in the form of $\dfrac{p}{q}$ where p and q both are integers, and $q \ne 0$
Now, we know that each and every whole number is a rational number as it can be expressed in the form of $\dfrac{p}{q}$ where p and q both are integers, and $q \ne 0$
So, the number 23 is also a rational number.
Thus, statement D is also correct.
Now, as 23 is a rational number, it can’t be an irrational number.
So, the number 23 is not an irrational number.
Thus, statement C is incorrect
Now, we know that each and every rational or irrational number is a real number.
So, the number 23 being a rational number is also a real number.
Thus, statement B is also correct.
Therefore we have statement A, B, D as correct and statement C is incorrect.
Hence, option A is correct.

Note: Students must not get confused with the basic terms of the number system. Students must know the definition of each and every type of number and also the inclusion and exclusion of a set of numbers in another.
On top, we have Real numbers, which are all those numbers which can be represented on the number line. Then real numbers have to subparts, Rational and irrational numbers.
A rational number can be defined as a number which can be expressed in the form of $\dfrac{p}{q}$ where p and q both are integers, and $q \ne 0$
And irrational is the opposite, for example:
$\sqrt 5 ,\pi $
Further, Rational numbers include whole numbers, fraction, decimal numbers etc.
So, students must remember this hierarchy while attempting these types of problems.