Is 230 a Prime Number?

There are two main types of numbers —

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 230 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 230 has more than two factors, it is not a prime number.

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

Here are a few methods:

• 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 numbers as prime or composite.

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

Let’s check whether 230 is prime or composite.

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

Step 2: Divide 230 by 2. It is divisible by 2, so 2 is a factor of 230.

Step 3: Divide 230 by 3. It is not divisible by 3, so 3 is not a factor of 230.
 

Step 4: You can simplify checking divisors up to 230 by finding the square root value. We then need to only check divisors up to the square root value.
 

Step 5: When we divide 230 by 2, 5, and 10, it is divisible by 2, 5, and 10. Since 230 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. This is called the Divisibility Test Method.
 

Divisibility by 2: The number in the ones' place is 0. Zero is an even number, so 230 is divisible by 2.

Divisibility by 3: The sum of the digits in the number 230 is 5. Since 5 is not divisible by 3, 230 is not divisible by 3.
 

Divisibility by 5: The unit’s place digit is 0. Therefore, 230 is divisible by 5.
 

Divisibility by 11: In 230, the difference between the sum of the digits in odd positions (2 + 0) and the sum of the digits in even positions (3) is 1. Since 1 is not divisible by 11, 230 is not divisible by 11. Since 230 is divisible by 2 and 5, it has more than two factors. Therefore, it is a composite number.
 

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

In this method, the following steps are used:

Step 1: Write numbers from 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. 230 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 multiplying those factors to obtain the original number.
 

Step 1: We can write 230 as 2 × 115.
 

Step 2: In 2 × 115, break 115 into 5 × 23.
 

Step 3: Now we get the product consisting of only prime numbers. Hence, the prime factorization of 230 is 2 × 5 × 23.

• Composite numbers: Natural numbers greater than 1 that are divisible by more than 2 numbers are called composite numbers. For example, 12 is a composite number because it is divisible by 1, 2, 3, 4, 6, and 12.
   
• Prime factorization: The process of expressing a number as the product of its prime factors. For example, the prime factorization of 30 is 2 × 3 × 5.
   
• Divisibility: A number is divisible by another if you divide them with no remainder. For example, 20 is divisible by 5.
   
• Sieve of Eratosthenes: An ancient algorithm used to find all primes up to a specified integer. Factors: Numbers that divide another number exactly without leaving a remainder. For example, the factors of 8 are 1, 2, 4, and 8.