Question

How many even prime numbers are there in the number system?

Answer 1

Hint: Even number is basically a number which is divisible by 2 and prime number is a number which has only two factors: the given number and ‘1’. Both are natural numbers and prime numbers are defined for numbers greater than 1. Use these fundamental concepts to get the prime number, which is an even number.
Complete step-by-step answer:
As we need to determine the even prime number i.e. the number which is a prime number and an even number as well. So, for getting that number, let us just take a look at the definition part of them.
Even number: Even numbers are natural numbers which are divisible by 2, where natural numbers are defined as counting numbers (1,2,3,4,5……). So, in other words a natural number which has a factor of 2 is an even number i.e. any even number will be a multiple of 2. So, we can observe that the even numbers will be given as (multiple of 2)
2, 4, 6, 8, 10……………….
Now coming to the definition of a prime number. It is given as:
Prime number: Any natural number greater than 1 which has only two factors 1 and the number itself is known as a prime number. It means any prime number will not be a multiple of any number except 1 and the number itself. Hence, we can start verifying the numbers as:
$2\to$ 2 has only two factors 1 and 2. So it should be a prime number
3 $\to$ 3 has only two factors 1 and 3. So, it should be a prime number
4 $\to$ 4 has 3 factors: 1, 2, 4. So, it should not be a prime number
5 $\to$ 5 has 2 factors 1 and 5. So, it will be a prime number
So, prime numbers are given as
2, 3, 5, 7, 11, 13……….
Now, we can observe that 2 is the least prime number and it is an even number (least even number) as well because the even numbers other than ‘2’ will be greater than ‘2’ and will be a multiple of 2 as well. It means all the other even numbers will have at least three factors, so they can not be a prime number. Hence, there is only one number ‘2’ which is prime and even both.
Hence, the answer of the given question is 1.
Note: One may get confused that how any even number can be a prime number, as any even number will be a multiple of 2 and hence, he/she can answer that there is no any number which is prime and even both, which is wrong. 2 is a number which is divisible by ‘2’; even and prime as well because 2 has only two factors 1 and 2. So, as per the definition of prime number 2 will act as prime number as well.