Question

Which of the following numbers is composite?
$\left( a \right) 1$
$\left( b \right) 4$
$\left( c \right) 2$
$\left( d \right) 3$

Answer 1

Hint: We know that a number that does not have positive divisors that are not $1$ and the number itself is called a prime number while a number that has at least one positive divisor that is not $1$ and the number itself is called a composite number.

Complete step by step solution:
We are asked to find the composite number among the given composite numbers.
We know that a composite number has more than two divisors for $1$ and the number itself are its divisors by default. So, we can say that a composite number has at least one positive divisor that is neither $1$ nor the number itself.
We define a prime number as a number that has only two positive divisors. And they are $1$ and the number itself.
So, let us find the divisors of each of the given numbers so that we can see which of these numbers contain more than two positive divisors. Or in other words, which of these numbers has a positive divisor other than $1$ and the number itself.
Let us consider $1.$ We know that $1$ has only one positive divisor. That is $1.$ Also, we know that $1$ is considered neither a prime number nor a composite number.
Let us move on. We know that the factors of $4$ are $1,2$ and $4$ itself. So, $4$ has a positive divisor other than $1$ and $4$ itself.
We know that $2$ does not have a positive divisor other than $1$ and $2$ itself. That means, $2$ is a prime number. And it is the least prime number.
We know that $3$ also does not have a positive divisor other $1$ and $3$ itself. Therefore, $3$ is a prime number.
Hence $4$ is the composite number.

So, the correct answer is “Option B”.

Note: We know that $2$ is the only even number which is a prime number for the rest of the even numbers are multiples of $2.$ This does not mean that every odd number is a prime number. For example, $9$ has a divisor $3.$