Question

The total number of even prime numbers is
(a) 0
(b) 1
(c) 2
(d) None of these.

Answer 1

Hint: We solve this problem by using the definition of prime number. A prime number is defined as a number having only two factors which are 1 and itself. From this definition we find the total number of even numbers that are primes.

Complete step-by-step answer:
We know that the prime number is defined as a number having only two factors which are 1 and itself.
Let us consider the first even number that is 2.
Now, the factors of 2 are written as
\[2=1\times 2\]
Here, we can say that the number 2 has factors 1 and 2 only. So, 2 is a prime number.
Now let us consider any other even number other than 2 as\['k'\].
Here, we can write the number\['k'\]as follows
\[\Rightarrow k=2\times n\]
Here,\['n'\]is some other number.
Now, we can write the factors of\['k'\]as
\[\begin{align}
  & \Rightarrow k=1\times k \\
 & \Rightarrow k=2\times n \\
\end{align}\]
Here, we can say that the number\['k'\]has more than two factors. So,\['k'\]is not a prime number.
Therefore, we can conclude that there is only one even prime number which is 2.

So, the correct answer is “Option (b)”.

Note: This question can be explained by the standard result that is there is one and only one even prime number that is 2. This is the standard result of prime numbers.
In this question students mainly make mistakes in selecting the option.
We are asked to find the number of even prime numbers not the even prime number.
So the correct answer will be option (b) not the option (c).
But students will select option (c) in a hurry. So, taking the option is important.