Question

Is \[27\] prime or composite?

Answer 1

Hint: We use the concepts of prime numbers and definitions of prime numbers to solve this problem. We also use divisibility rules to solve this problem. We will look at some examples of prime numbers and also some examples of composite numbers and from those, we will find the solution for this problem.

Complete answer:
A prime number is a natural number greater than 1, which is divisible only by 1 and the number itself.
So, in other words, numbers which have only two divisors have been called prime numbers.
All other numbers other than prime numbers are called composite numbers.
For example, take the natural number 2.
So, the number 2 is only divisible by two numbers which are 1 and 2. So, 2 is a prime number.
Take another example 5, which is also having two divisors 1 and 5. So, 5 is also a prime number.
These are the few prime numbers:
\[2,3,5,7,11,13,17,19,23,29,31,......\]
Every composite number can be written as a product of prime numbers.
For example, take number 24, which is a composite number.
So, we can write 24 as, \[24 = 2 \times 2 \times 2 \times 3\]
Now, take the number \[27\].
According to divisibility rule of 3, if the sum of digits of a number is a multiple of 3, then the number is divisible by 3.
So, in number 27, the sum of its digits is \[2 + 7 = 9\] which is a multiple of 3.
So, 27 is divisible by 3. And also divisible by 1 and 27 too.
So, divisors of 27 are \[1,3,9,27\]

So, it has more than two divisors and by this reason, we can conclude that 27 is a composite number.

Note: The number 1 is neither a prime number nor a composite number. And the number 2 is the least prime number. And the number 4 is the least composite number. If a number has an even number as its last digit, then it is divisible by 2. This is the divisibility rule of 2.