Question

Which number has only two factors: \[21\], \[23\], \[25\], \[27\]?

Answer 1

Hint: To find the number which has only two factors out of \[21\], \[23\], \[25\], \[27\], we will use 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 prime number and out of them we will find the number which has two factors.

Complete step-by-step solution:
For finding 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,
\[21\] has three factors i.e., \[1,3{\text{ and 7}}\].
\[23\] has only two factors i.e., \[1{\text{ and 23}}\].
\[{\text{25}}\] has three factors i.e., \[1,5{\text{ and 25}}\].
\[27\] has four factors i.e., \[1,3,9{\text{ and 27}}\].
We can see that \[21,{\text{ }}25{\text{ and 27}}\] has more than two factors and only \[23\] has two factors.
Therefore, \[23\] has only two factors.

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.