Question

Is a multiple of the prime number $3$ is also a prime number?

Answer 1

Hint: Here we have asked that a multiple of $3$ is also a prime number.Prime numbers are those numbers whose only factors are $1$ and the number itself. $3$ is a prime number as it can be divided by only $1$ and $3$. If a number has more than two factors then it is a composite number.

Complete step by step answer:
Numbers can be divided into two types on the basis of factors they have. These two types of numbers are prime numbers and composite numbers. A prime number is a number which has only two factors $1$ and the number itself whereas composite numbers number is a number which has more than two factors.

Prime numbers are the numbers which have only two factors $1$ and the number itself which means that the number can be divided by itself $1$ and itself. All prime numbers are odd numbers except from $2$. Every non-prime prime number is a composite number.
For example- $2,\,\,3,\,\,5,\,\,7, \ldots $ etc are some of the prime numbers. The multiple of prime numbers can never be a prime number as they have a factor other than $1$ and the number itself or we can say that they can be divided by a number other than $1$ and the number itself.

$3$ is a prime number as it cannot be divided by the number other than $1$ and $3$. The multiple of $3$ can never be a prime number as the number has a factor other than $1$ and the number itself or we can say that the number is divided by the number other than $1$ and the number itself as the number is a multiple of $3$ so it can be divided by $3$.

Therefore, the multiple of $3$ can never be a prime number; it will be a composite number as it has more than two factors.

Note: The number $2$ is only a prime number which is even except $2$ all prime numbers are odd numbers. The numbers $0$ and $1$ are neither considered as prime numbers nor composite numbers. Composite numbers are the numbers which can be obtained by multiplying two smallest positive numbers. For example- $4,6,9,10, \ldots $ are composite numbers as they have more than two factors. There are two types of composite numbers- odd composite numbers and even composite numbers.