Is 293 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 have a few properties, such as:

• 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 293 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 293 has exactly two factors, it is a prime number. There are several methods 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 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 is prime. 
   
• If the count is more than 2, then the number is composite.

Let’s check whether 293 is prime or composite.

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

Step 2: Check divisibility by numbers greater than 1 up to the square root of 293 (approximately 17.1).

Step 3: 293 is not divisible by any numbers from 2 to 17 without leaving a remainder.

Since 293 has only 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. For 293:

Divisibility by 2: 293 is an odd number, so it is not divisible by 2. 

Divisibility by 3: The sum of the digits in 293 is 14. Since 14 is not divisible by 3, 293 is not divisible by 3.

Divisibility by 5: The unit’s place digit is 3. Therefore, 293 is not divisible by 5. 

Divisibility by 7, 11, 13, and 17: 293 is not divisible by these numbers as verified by actual division.

Since 293 is not divisible by any numbers other than 1 and itself, it is a prime number.

The prime number chart is a tool created using a method called “The Sieve of Eratosthenes.” In this method, we follow the steps below:

Step 1: Write numbers in a specific range (e.g., 1 to 1000).

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 the list. Through this process, we will have a list of prime numbers.

Since 293 appears in the list of prime numbers, it confirms that 293 is a prime number.

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

For 293, the process is straightforward: Since 293 is not divisible by any prime numbers up to its square root, it cannot be broken down further, and thus, 293 itself is a prime factor. Therefore, the prime factorization of 293 is simply 293.

• Prime numbers: Natural numbers greater than 1 that have no divisors other than 1 and themselves. For example, 293 is a prime number. 
   
• Composite numbers: Natural numbers greater than 1 that have more than 2 divisors. For example, 12 is a composite number. 
   
• Divisibility test: A method to determine if one number is divisible by another without performing division.
   
• Prime factorization: The process of breaking down a number into its prime components.
   
• Sieve of Eratosthenes: An ancient algorithm used to find all prime numbers up to a specified integer.