Is 296 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 the following 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 because they have only one common factor, which is 1.
   
• Since 296 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 296 has more than two factors, it is not a prime number. Several methods are used to distinguish between prime and composite numbers, including:

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

The counting divisors method involves counting the number of divisors to categorize numbers as prime or composite. Based on the count of the divisors, we categorize numbers as follows:

• 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 296 is prime or composite.

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

Step 2: Divide 296 by 2. It is divisible by 2, so 2 is a factor of 296.

Step 3: Divide 296 by 3. It is not divisible by 3, so 3 is not a factor of 296.

Step 4: Simplify checking divisors up to 296 by finding the square root. We only need to check divisors up to the square root.

Step 5: When we divide 296 by 2, 4, 8, 37, and 74, it is divisible by these numbers.

Since 296 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 6, an even number, making 296 divisible by 2. 

Divisibility by 3: The sum of the digits in 296 is 17, which is not divisible by 3, so 296 is not divisible by 3.

Divisibility by 5: The unit’s place digit is 6, so 296 is not divisible by 5.

Divisibility by 7: Double the last digit (6 × 2 = 12). Subtract it from the rest of the number (29 - 12 = 17). Since 17 is not divisible by 7, 296 is not divisible by 7.

Divisibility by 11: The difference between the sum of the digits in odd positions (2 + 6) and even positions (9) is 1, so 296 is not divisible by 11.

Since 296 is divisible by more than two numbers, 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 numbers from 1 to 100 in 10 rows and 10 columns.

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

Step 3: Mark 2 because it is a prime number and cross out all multiples of 2.

Step 4: Mark 3 because it is a prime number and cross out all multiples of 3.

Step 5: Repeat this process until you have a 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 includes 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. 296 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 and then multiplying those factors to obtain the original number.

Step 1: We can write 296 as 2 × 148.

Step 2: In 2 × 148, 148 is a composite number. Further, break down 148 into 2 × 74.

Step 3: Then break down 74 into 2 × 37. Now we get the product consisting of only prime numbers.

Hence, the prime factorization of 296 is 2 × 2 × 2 × 37.

• 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 numbers: Numbers greater than 1 with no divisors other than 1 and themselves. For example, 5 is a prime number because it is only divisible by 1 and 5.
   
• Sieve of Eratosthenes: An ancient algorithm used to find all prime numbers up to a specific integer.
   
• Prime factorization: The process of breaking down a number into its prime factors.
   
• Divisibility rules: Guidelines for determining whether one number is divisible by another without performing division.