Is 1117 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 1117 has only two factors, 1 and 1117, it is a prime number.
  
  

The characteristic of a prime number is that it has only two divisors: 1 and itself. Since 1117 has exactly two factors, it is a prime number. Several methods can be used to determine if a number is prime:
 

• 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 1117 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 1117 (approximately 33.4).

Step 3: 1117 is not divisible by any numbers other than 1 and itself.

Since 1117 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.

1117 is not divisible by 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, or 31 (all primes up to the square root of 1117).

Since 1117 is not divisible by any numbers other than 1 and itself, it has only two factors. Therefore, 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.

Step 2: Leave 1 without marking, 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 required range.

Through this process, you can identify prime numbers. Since 1117 is not divisible by any prime numbers up to its square root, it remains unmarked and is confirmed as 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: Attempt to divide 1117 by the smallest prime numbers.

Step 2: Since 1117 is not divisible by any primes up to its square root, it cannot be broken down into prime factors. Hence, 1117 is a prime number as it cannot be factored further.

• Prime Number: A natural number greater than 1 that has no positive divisors other than 1 and itself.
   
• Composite Number: A natural number greater than 1 that is not prime because it has more than two unique factors.
   
• Divisibility: The ability for one number to be divided by another without leaving a remainder.
   
• Co-prime Numbers: Two numbers that have no common factors other than 1.
   
• Sieve of Eratosthenes: An ancient algorithm used to find all prime numbers up to a specified integer.