Is 1115 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.
   
• As 1115 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 1115 has more than two factors, it is not a prime number. Few methods are used to distinguish between prime and composite numbers. These methods include: 

• 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 1115 is prime or composite.

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

Step 2: Divide 1115 by 2. It is not divisible by 2, so 2 is not a factor of 1115.

Step 3: Divide 1115 by 3. The sum of the digits (1 + 1 + 1 + 5 = 8) is not divisible by 3, so 3 is not a factor of 1115.

Step 4: Divide 1115 by 5. The last digit is 5, which means it is divisible by 5.

Since 1115 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. It is called the Divisibility Test Method. 

Divisibility by 2: 1115 is not divisible by 2 as it's an odd number. 

Divisibility by 3: The sum of the digits in the number 1115 is 8. Since 8 is not divisible by 3, 1115 is also not divisible by 3. 

Divisibility by 5: The unit’s place digit is 5. Therefore, 1115 is divisible by 5. 

Divisibility by 7: Applying the divisibility rule for 7, 1115 divided by 7 does not result in an integer, so it is not divisible by 7. 

Divisibility by 11: The alternating sum of the digits (1 - 1 + 1 - 5 = -4) is not divisible by 11, so 1115 is not divisible by 11.

Since 1115 is divisible by 5, it has more than two factors, making it a composite 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 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.

Since 1115 is greater than 100, we need to check against prime numbers up to its square root. It is not found 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. Then multiply those factors to obtain the original number.

Step 1: We can start by dividing 1115 by 5, as it ends in 5.

Step 2: 1115 ÷ 5 = 223.

Step 3: Check if 223 is a prime number. It is divisible by 1 and itself, so 223 is prime.

Hence, the prime factorization of 1115 is 5 × 223.

• Composite numbers: Natural numbers greater than 1 that are divisible by more than 2 numbers are called composite numbers. For example, 15 is a composite number because it is divisible by 1, 3, 5, and 15. 
  
   
• Prime factorization: The process of expressing a number as the product of its prime factors. For example, the prime factorization of 18 is 2 × 3 × 3.
  
   
• Divisibility: A number is divisible by another if it can be divided by that number without leaving a remainder. 
  
   
• Sieve of Eratosthenes: An ancient algorithm used to find all prime numbers up to any given limit.
  
   
• Co-prime numbers: Two numbers that have only 1 as their common factor. For example, 9 and 14 are co-prime.