Is 1187 a Prime Number?

There are two main types of numbers—

prime numbers and composite numbers, depending on the number of factors they have.

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 distinct 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 numbers because they have only one common factor, which is 1.
   
• Since 1187 has exactly two factors, it is a prime number.
  
  

The characteristic of a prime number is that it has only two divisors: 1 and itself. Since 1187 has exactly two factors, it is a prime number. Various methods can be used to identify prime numbers, including: 

• 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 is prime. 
   
• If the count is more than 2, then the number is composite.

Let’s check whether 1187 is prime or composite.

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

Step 2: Divide 1187 by numbers up to its square root to check for additional factors. None of these divisions result in a whole number, confirming that 1187 has no divisors other than 1 and itself.

Since 1187 has exactly 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. Testing divisibility by common factors: 

Divisibility by 2: 1187 is odd, so it is not divisible by 2. 

Divisibility by 3: The sum of the digits in 1187 is 17, which is not divisible by 3. 

Divisibility by 5: The last digit is not 0 or 5, so 1187 is not divisible by 5. 

Divisibility by 7, 11, 13, etc.: Further checks show no divisibility by these primes.

Since 1187 is not divisible by any number other than 1 and itself, 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 these steps: 

Step 1: Write numbers in a sequence. 

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 for primes up to the square root of the largest number in the sequence.

1187 is not crossed out in this process, confirming it is a prime number.

Prime factorization is a process of expressing a number as a product of its prime factors. Since 1187 cannot be divided evenly by any prime number up to its square root, it cannot be factored further. Therefore, 1187 is a prime number.

• Prime Numbers: Natural numbers greater than 1 that have no divisors other than 1 and themselves. For example, 5 is a prime number.
   
• Composite Numbers: Natural numbers greater than 1 that have more than two factors. For example, 12 is a composite number.
   
• Divisibility Rules: Guidelines that help determine if one number is divisible by another without performing division.
   
• Prime Factorization: The expression of a number as a product of prime numbers. For example, the prime factorization of 30 is 2 × 3 × 5.
   
• Sieve of Eratosthenes: An ancient algorithm used to find all prime numbers up to a specific integer.