Question

What is the smallest composite number: \[12\], \[59\], \[8\], or \[43\]?

Answer 1

Hint: To find the smallest composite number out of the given numbers we have to first understand the concept of prime numbers and composite numbers. Then we will observe each given number and will try to categorise it according to the definition of composite number and out of them we will find the smallest composite number.

Complete step-by-step answer:
To find the smallest composite number out of the given numbers we have to first understand the concept of prime numbers and composite numbers.
Prime Numbers:
A prime number is a natural number that is counting numbers, that has only two factors i.e., a prime number is divisible by only two numbers. These two numbers are \[1\] and the number itself. For example, \[3\] is only divisible by \[1\] and \[3\] itself i.e., it has only two factors \[1\] and \[3\]. So, \[3\] is a prime number.
Composite Numbers:
A Composite number is a natural number that is counting numbers, that has more than two factors i.e., a Composite number is divisible by more than two numbers. Therefore, we can say that a natural number which is not a prime is a composite number. For example, \[4\] is divisible by \[1,2\] and \[4\] itself. So, it is a composite number.
From the given numbers,
\[12\] is divisible by \[2,3,4{\text{ and }}6\].
\[59\] is divisible by only \[1{\text{ and }}59\].
\[8\] is divisible by \[2,4{\text{ and }}8\].
\[43\] is divisible by only \[1{\text{ and }}43\].
We can see that only \[12\] and \[8\] have more than two factors. Therefore, \[12\] and \[8\] are composite numbers out of \[12\], \[59\], \[8\] and \[43\].
Also, as \[8 < 12\]. So, \[8\] is the smallest composite number from the given numbers.
Therefore, \[8\] is the smallest composite number in \[12\], \[59\], \[8\] and \[43\].
So, the correct answer is “8”.

Note: Every number is either a prime number or composite number except \[1\], because \[1\] has only one factor which is \[1\] itself. Also, note that the smallest prime number is \[2\] and the smallest composite number is \[4\]. To solve these types of problems the most important point one should keep in mind is the definition of prime numbers and composite numbers.