Is 27 a Prime Number?

There are many tests to find if 27 is a prime number or not. But since 27 is a small number, it is easy to test. We can see that 27 has 4 divisors: 1, 3, 9 and 27. But a prime number has only 2. So, 27 cannot be a prime number.
 

Here are some methods that can prove why 27 is not a prime number. Let us look at these methods and learn them step by step.

In this method, we will find out the number of divisors that can divide the given number evenly. Based on the count of divisors, we will categorize the number as either prime or composite.

If the count of divisors is 2, then the number is a prime number. 

If the count of divisors is more than 2 then the number is composite.

Step 1: Note that every number, including 27, is divisible by 1.

Step 2: Divide 27 by 2, as it is not divisible by 2. So 2 is not a factor of 27.

Step 3: Then divide 27 by 3 and it can be divided by 3. So 3 is a factor of 27.

Step 4: Likewise, we have to check up to the square root of 27.

√27=5.1961 = 5 (approximately)

Step 5: As we can find 27 is divided by 3 and 9.

Hence, 27 is not a prime number, because 27 has more than 2 divisors.
 

We will be checking the divisibility of 27 by a set of numbers. If divisible by any of the numbers, 27 is not a prime number.

Divisibility by 2: For a number to be divisible by 2, it has to be an even number. But 27 is not an even number. Hence, it is not divisible by 2. 

Divisibility by 3: The number should be a multiple of 3 to be divisible by 3. We have to add 2 and 7, to check. We get 9 when we add. Likewise, we can see that 9 is a multiple of 3 when we multiply 3 × 3. This shows that 27 is divisible by 3.

Divisibility by 5: 27 is not divisible by 5 as it does not end with 0 or 5.

This shows that 27 is divisible by 3, apart from 1 and 27. Since this violates the rules of a prime number, 27 is not a prime number.
 

First let us look at the prime numbers from 1 to 100: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89 and 97. As we can see, 27 does not appear in the list. This confirms that 27 is not a prime number.
 

Prime factorization helps determine the prime factors of numbers. For instance, 27 is a composite number because it has a prime factor of 3. Indeed, 27 can be presented as 3 × 9 = 27, thus showing it has factors other than 1 and 27.
 

• Prime Factorization: Prime factorization is one of the operations of a mathematical expression in which a number is expressed as the product of its prime factors. For example, the prime factorization of 6 is 2 × 3.

• Multiple: The product of two numbers is called multiple. Some multiples of 27 are 27, 54, 81, 108, 135 and so on.

• Composite numbers: Composite numbers are natural numbers that are greater than 1 and have more than 2 factors other than 1 and itself. Some examples of composite numbers are 4, 6, and 9.

• Whole Numbers: If a number is an integer, and it has no fraction, then it is called a whole number. Some examples for whole numbers are 1, 2, 3, 4, 5, and so on.