Is 228 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, 5 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, 8 is divisible by 1, 2, 4, and 8, 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 that is 1.
   

          As 228 has more than two factors, it is not a prime number.

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

Since 228 has more than two factors, it is not a prime number.

A 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 228 is prime or composite.
 

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

Step 2: Divide 228 by 2. It is divisible by 2, so 2 is a factor of 228.
 

Step 3: Divide 228 by 3. It is divisible by 3, so 3 is a factor of 228.
 

Step 4: You can simplify checking divisors up to 228 by finding the square root value. We then need to only check divisors up to the square root value.
 

Step 5: When we divide 228 by 2, 3, 4, 6, 12, and other numbers, it is evident that 228 has more than 2 divisors. Since 228 has more than 2 divisors, it is a composite 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: The number in the ones' place value is 8. Eight is an even number, which means that 228 is divisible by 2.
 

Divisibility by 3: The sum of the digits in the number 228 is 12 (2+2+8=12). Since 12 is divisible by 3, 228 is also divisible by 3.
 

Divisibility by 5: The unit’s place digit is 8. Therefore, 228 is not divisible by 5.
 

Divisibility by 7: The last digit in 228 is 8. To check divisibility by 7, double the last digit (8 × 2 = 16). Then, subtract it from the rest of the number (22 - 16 = 6). Since 6 is not divisible by 7, 228 is also not divisible by 7.
 

Divisibility by 11: In 228, the sum of the digits in odd positions is 10 (2+8), and the sum of the digits in even positions is 2. The difference is 8, which is not divisible by 11. Since 228 is divisible by 2 and 3, it has more than two factors. Therefore, it is a composite 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 1 to 100 in 10 rows and 10 columns.
 

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 table consisting of marked and crossed boxes, except 1. Through this process, we will have a list of prime numbers from 1 to 100. The list is 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. 228 is not present in the list of prime numbers, so it is a composite number.

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

Then multiply those factors to obtain the original number.
 

Step 1: We can write 228 as 2 × 114.
 

Step 2: In 2 × 114, 114 is a composite number. Further, break the 114 into 2 × 57.
 

Step 3: Now, break 57 into 3 × 19, both of which are prime numbers. Hence, the prime factorization of 228 is 2 × 2 × 3 × 19.

• Composite numbers: Natural numbers greater than 1 that are divisible by more than 2 numbers are called composite numbers. For example, 228 is a composite number because it is divisible by multiple numbers such as 1, 2, 3, 4, 6, 12, 19, 38, 57, 76, 114, and 228.
   
• Factors: The numbers that divide the number exactly without leaving a remainder are called factors. For example, the factors of 228 are 1, 2, 3, 4, 6, 12, 19, 38, 57, 76, 114, and 228.
   
• Prime Factorization: The process of expressing a number as a product of its prime factors. For example, the prime factorization of 228 is 2 × 2 × 3 × 19.
   
• Divisibility: The ability of one number to be divided by another without a remainder. For example, 228 is divisible by 2 because it leaves no remainder.
   
• Prime number: A natural number greater than 1 that is not divisible by any numbers other than 1 and itself. For example, 19 is a prime number.