Question

Which of the following is a prime number?
A.$33$
B.$81$
C.$93$
D.$97$

Answer 1

Hint- In order to get the grip with this question first we have to elaborate the term prime number and we will continue to get the prime number among all the options according to its definition or property.

Complete step-by-step solution -
Prime numbers are positive integer numbers that only have two variables, 1 and the integer itself. Factors of $6$, for example, are $1,2,3$ and $6$ which are four factors in total. But only $1$ and $7$ are prime factors, totally two. $7$ is indeed a prime number but $6$ is not, instead it is a composite number. But keep in mind that $1$ is neither prime nor composite.
We can also say that the prime numbers are the numbers, divisible only by $1$ or the number itself. Another way to describe it is that it is a positive number or integer that is not a consequence of any two other positive integers. There is no defined formula to find out whether or not a number is prime (except for a certain range), other than to find its factors
Now, take option A
$33 = 11 \times 3$,
Therefore, $33$ has two factors as $11$ and $3$ so it is not a prime number.
By considering option B
$81 = 9 \times 9$ or $3 \times 3 \times 3 \times 3$,
Therefore, $81$ also has multiple factors so it is not a prime number.
By taking option C
$93 = 31 \times 3$,
Therefore, $93$ also has two factors as $31$ and $3$, so it is not a prime number.
By considering option D
$97 = 97 \times 1$
Consequently, $97$ is the positive integer with only two factors, $1$ and the integer itself as $97$.
Hence option D is the correct answer.

Note- A prime number is a natural number greater than $1$ that is not a product of two smaller natural numbers. A natural number greater than $1$ that is not prime is called a composite number. For example, $7$ is prime because the only ways of writing it as a product $1 \times 7$or $7 \times 1$, involve $7$itself.