Is 232 a Prime Number?

Numbers can generally be categorized as prime numbers or composite numbers based on their factors.

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

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

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

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

Prime numbers have specific properties:

• 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 232 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 232 has more than two factors, it is not a prime number.

Several methods can be used to distinguish between prime and composite numbers.
 

Some of these methods include:

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

In the counting divisors method, we count the number of divisors to categorize numbers as prime or composite.
 

Based on the count of the divisors, we categorize numbers:

• 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 232 is prime or composite.
 

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

Step 2: Divide 232 by 2. It is divisible by 2, so 2 is a factor of 232.
 

Step 3: Divide 232 by 3. It is not divisible by 3, so 3 is not a factor of 232.
 

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

Step 5: When we divide 232 by 2, 4, 8, and 29, it is divisible by 2, 4, and 8. Since 232 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 value is 2, which means that 232 is divisible by 2.
 

Divisibility by 3: The sum of the digits in the number 232 is 7. Since 7 is not divisible by 3, 232 is also not divisible by 3.
 

Divisibility by 5: The unit’s place digit is 2. Therefore, 232 is not divisible by 5.

Divisibility by 7: To check divisibility by 7, double the last digit (2 × 2 = 4). Then, subtract it from the rest of the number (23 - 4 = 19). Since 19 is not divisible by 7, 232 is also not divisible by 7.
 

Divisibility by 11: In 232, the difference between the sum of the digits in odd positions and the sum of the digits in even positions is 0, which means 232 is divisible by 11. Since 232 is divisible by 2 and 11, 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, we follow these 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. Since 232 is not present in the list of prime numbers, it is a composite number.

Prime factorization is a process of breaking down a number into prime factors and then multiplying those factors to obtain the original number.

Step 1: We can write 232 as 2 × 116.
 

Step 2: In 2 × 116, 116 is a composite number. Further, break 116 into 2 × 58.
 

Step 3: Break 58 into 2 × 29.
 

Step 4: Now we get the product consisting of only prime numbers. Hence, the prime factorization of 232 is 2 × 2 × 2 × 29.
 

• 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 12 is divisible by 1, 2, 3, 4, 6, and 12.
   
• Co-prime numbers: Two numbers are co-prime if their greatest common divisor is 1. For example, 8 and 15 are co-prime because they have no common factors other than 1.
   
• Prime factorization: The expression of a number as the product of its prime factors. For example, the prime factorization of 18 is 2 × 3 × 3.
   
• Divisibility rules: Simple rules to determine whether a number is divisible by another without performing full division.
   
• Sieve of Eratosthenes: An ancient algorithm for finding all prime numbers up to a specified integer.