Is 233 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. Since 233 has only two factors, it is a prime number.
 

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

Since 233 has exactly two factors, it is 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 233 is prime or composite.

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

Step 2: Check divisibility by numbers up to the square root of 233 (approximately 15.26).
 

Step 3: 233 is not divisible by any number other than 1 and itself (2, 3, 5, 7, 11, and 13). Since 233 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: 233 is an odd number, so it is not divisible by 2.
 

Divisibility by 3: The sum of the digits in the number 233 is 8.

Since 8 is not divisible by 3, 233 is not divisible by 3.
 

Divisibility by 5: The unit’s place digit is 3, not 0 or 5, so 233 is not divisible by 5.
 

Divisibility by 7, 11, 13: Applying the divisibility rules for these numbers, 233 is not divisible by any of them. Since 233 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 numbers in a grid format, for example, from 1 to 250.
 

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

Step 3: Mark 2 and cross out all the multiples of 2.
 

Step 4: Mark 3 and cross out all the multiples of 3.

Step 5: Repeat this process for subsequent numbers. Through this process, we will have a list of prime numbers. Since 233 is not crossed out, it remains a prime 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: Try dividing 233 by the smallest prime number, 2. It is not divisible.
 

Step 2: Try the next primes, 3, 5, 7, 11, and 13. 233 is not divisible by any of these.

Since 233 cannot be factored into any smaller prime numbers, it is itself a prime number.

• Prime Numbers: Natural numbers greater than 1 that have no divisors other than 1 and themselves. For example, 233 is a prime number.
   
• Composite Numbers: Natural numbers greater than 1 that are divisible by more than two numbers. For example, 12 is a composite number.
   
• Divisibility: The ability of a number to be divided by another number without leaving a remainder.
   
• Sieve of Eratosthenes: An ancient algorithm used to find all prime numbers up to a specified integer.
   
• Perfect Square: A number that is the square of an integer. For example, 16 is a perfect square because it is 4 squared.