Is 1097 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 1097 does not have more than two factors, it is indeed a prime number.

The characteristic of a prime number is that it has only two divisors: 1 and itself. Since 1097 has exactly two factors, it is a prime number. 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 numbers as prime or composite. - 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 1097 is prime or composite.

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

Step 2: Check divisibility by numbers up to the square root of 1097. The approximate square root of 1097 is 33.

Step 3: 1097 is not divisible by any integer between 2 and 33.

Since 1097 has exactly 2 divisors (1 and 1097), 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: 1097 is not divisible by 2, as it is an odd number. 

Divisibility by 3: The sum of the digits in 1097 is 17, which is not divisible by 3.

Divisibility by 5: The unit’s place digit is 7, so 1097 is not divisible by 5. 

Divisibility by 7, 11, 13, etc.: 1097 is not divisible by these primes as tested by successive division.

Since 1097 is not divisible by any of these numbers, 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 from 1 to 1200 in rows and 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.

1097 is marked as a prime number, confirming its status.

Prime factorization is a process of breaking down a number into prime factors. Then multiply those factors to obtain the original number. Since 1097 is a prime number, it cannot be factored further into other prime numbers. The only factors of 1097 are 1 and 1097 itself.

• Prime numbers: Natural numbers greater than 1 that have no divisors other than 1 and themselves.
   
• Composite numbers: Numbers that have more than two distinct factors. 
   
• Divisibility rules: Guidelines that help determine if a number is divisible by another without performing division. 
   
• Sieve of Eratosthenes: An ancient algorithm used to find all prime numbers up to a specified integer. 
   
• Prime factorization: Breaking down a composite number into a product of its prime factors.