Is 227 a Prime Number?

There are two types of numbers, mostly —

Prime numbers and composite numbers, depending on the number of factors.

A prime number is a natural number that is divisible only by 1 and itself.

For example, 3 is a prime number because it is divisible by 1 and itself.

A composite number is a positive number that is divisible by more than two numbers.

For example, 6 is divisible by 1, 2, 3, and 6, making it a composite number.

Prime numbers follow a few properties like:

• Prime numbers are positive numbers always greater than 1.
   
• 2 is the only even prime number.
   
• They have only two factors: 1 and the number itself.
   
• Any two distinct prime numbers are co-prime numbers because they have only one common factor, which is 1.
   

As 227 has exactly two factors, it is a prime number.

The characteristic of a prime number is that it has only two divisors: 1 and itself.

Since 227 has exactly two factors, it is a prime number.

Few methods are used to distinguish between prime and composite numbers.

A few methods are:

• Counting Divisors Method
   
• Divisibility Test
   
• Prime Number Chart
   
• Prime Factorization

The method in which we count the number of divisors to categorize the numbers as prime or composite is called the counting divisors method.

Based on the count of the divisors, we categorize prime and composite numbers.

• If there is a total count of only 2 divisors, then the number would be prime.
• If the count is more than 2, then the number is composite.

Let’s check whether 227 is prime or composite.
 

Step 1: All numbers are divisible by 1 and itself.
 

Step 2: Divide 227 by 2. It is not divisible by 2, so 2 is not a factor of 227.
 

Step 3: Divide 227 by 3. It is not divisible by 3, so 3 is not a factor of 227.
 

Step 4: You can simplify checking divisors up to 227 by finding the square root value. We then need to only check divisors up to the root value.
 

Step 5: When we divide 227 by numbers up to its square root (approximately 15), it is not divisible by any number other than 1 and 227 itself. Since 227 has exactly 2 divisors, it is a prime number.

We use a set of rules to check whether a number is divisible by another number completely or not. It is called the Divisibility Test Method.

Divisibility by 2: 227 is an odd number, so it is not divisible by 2.
 

Divisibility by 3: The sum of the digits in the number 227 is 11. Since 11 is not divisible by 3, 227 is also not             divisible by 3.
 

Divisibility by 5: The unit’s place digit is 7. Therefore, 227 is not divisible by 5.
 

Divisibility by 7: The last digit in 227 is 7. To check divisibility by 7, double the last digit (7 × 2 = 14). Then, subtract it from the rest of the number (22 - 14 = 8). Since 8 is not divisible by 7, 227 is also not divisible by 7.
 

Divisibility by 11: In 227, the difference between the sum of the digits in odd positions and the sum of the digits in even positions is 3. Since 3 is not divisible by 11, 227 is also not divisible by 11. Since 227 is not divisible by any number other than 1 and itself, it is a prime number.

The prime number chart is a tool created by using a method called “The Sieve of Eratosthenes.”

In this method, we follow the following steps.
 

Step 1: Write a range of numbers.
 

Step 2: Leave 1 without coloring or crossing, as it is neither prime nor composite.
 

Step 3: Mark 2 because it is a prime number and cross out all the multiples of 2.
 

Step 4: Mark 3 because it is a prime number and cross out all the multiples of 3.

Step 5: Repeat this process until you reach the end of your range. By using a prime number chart, we can confirm that 227 is a prime number because it does not get crossed out as a multiple of any other number.

Prime factorization is a process of breaking down a number into prime factors.

Then multiply those factors to obtain the original number.

Since 227 is only divisible by 1 and 227 itself without leaving a remainder, it cannot be broken down further into smaller prime factors.

Hence, the prime factorization of 227 is 227 itself.

• Prime numbers: Natural numbers greater than 1 that have no divisors other than 1 and themselves.
   
• Composite numbers: Natural numbers greater than 1 that are divisible by more than 2 numbers. 
   
• Divisibility rules: Guidelines that help to determine if one number is divisible by another without performing full division.
   
• Sieve of Eratosthenes: An ancient algorithm used to find all prime numbers up to a specified integer.
   
• Factors: The numbers that divide another number exactly without leaving a remainder.