Question

Which of the following is a prime number?
(A) $19$
(B) $20$
(C) $21$
(D) $22$

Answer 1

Hint: The given question is based upon the number system. There are different types of numbers in mathematics like odd, even, prime…… so on. To solve the given question we discuss all the possible cases that arise to identify whether the number is prime or not. Firstly, we apply the condition of even numbers on a particular number say $19$ then we apply another condition of prime number on the chosen number $19$. In that way we conducted the result for finding the exact prime number.

Complete step-by-step answer:
In a number system, there are different types of numbers like prime, even, odd and composite. Let us discuss about these
Even numbers: Even numbers are those which can be divisible by $2$ like $2,4,6,8,........{\text{ so on}}$.
Odd numbers: Odd numbers are those which cannot be divisible by $2$ like $3,5,7,........{\text{ so on}}$.
Prime number: Prime number are those which can be divisible itself and $1$ .
Let us check if $19$ is prime or not for that discussion of all the cases of numbers as mentioned above.

\[{\mathbf{Case}}{\text{ }}{\mathbf{I}}:\] Even Number:
Diving $19$ by $2$ as we get $1$ remainder.
Here, we concluded that it is not an even number.
$\therefore $ It is not divisible by $2$

\[{\mathbf{Case}}{\text{ }}{\mathbf{II}}\]
For Odd number:
Let us check is $19$ divisible by any other Odd number or not.
In that case, consider a number $9$ where $9$ is an odd number.
We get $1$ remainder.
As it is not divisible by any odd number as well.

\[{\mathbf{Case}}{\text{ }}{\mathbf{III}}\]
Let dividing the number $19$ by itself.
As we can say that $19$ is divided by itself only, so it is a Prime Number.
In that way, we can conclude any number that is divisible by itself or $1$ like ...... $7,11,17,19,..............{\text{ so on}}{\text{.}}$

So, the correct answer is “Option A”.

Note: The above question is based upon the numbers. There are different types of numbers in Mathematics Prime Numbers are also included in that number. Prime numbers are used in several routines in Information technology like – Public Key cryptography. Also, one of the mostly used Prime numbers in computing is the RSA encryption system. The system they developed allows for the secure transmission of information like – Credit Card number Online.