Is 1185 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 1185 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 1185 has more than two factors, it is not a prime number. Several 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 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 1185 is prime or composite.

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

Step 2: Divide 1185 by 2. It is not divisible by 2, as it is odd.

Step 3: Divide 1185 by 3. The sum of the digits (1 + 1 + 8 + 5 = 15) is divisible by 3, so 3 is a factor of 1185.

Step 4: You can simplify checking divisors up to 1185 by finding the square root value. We then need to only check divisors up to this value.

Since 1185 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: 1185 is odd, so it is not divisible by 2. 

Divisibility by 3: The sum of the digits in the number 1185 is 15. Since 15 is divisible by 3, 1185 is divisible by 3. 

Divisibility by 5: The unit’s place digit is 5. Therefore, 1185 is divisible by 5. 

Divisibility by 7: Using the method of doubling the last digit and subtracting from the rest, 1185 gives 118 - 10 = 108, which is divisible by 7.

Since 1185 is divisible by 3, 5, and 7, it has more than two factors. Therefore, it is 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 numbers up to a certain range.

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

Step 3: Mark the smallest number greater than 1 that is not crossed and cross out all its multiples.

Step 4: Repeat this process until you reach the desired range. Through this process, we can determine whether a number like 1185 is prime.

Since 1185 is not present in any prime number chart, 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 write 1185 as 3 × 395.

Step 2: Further break down 395 as 5 × 79.

Step 3: Now we get the product consisting of only prime numbers.

Hence, the prime factorization of 1185 is 3 × 5 × 79.

• Composite numbers: Natural numbers greater than 1 that are divisible by more than 2 numbers are called composite numbers. For example, 18 is a composite number because 18 is divisible by 1, 2, 3, 6, 9, and 18.
   
• Prime factorization: The process of expressing a number as the product of its prime factors.
   
• Divisibility Rules: Guidelines for determining whether one number is divisible by another without performing division.
   
• Prime Numbers: Numbers greater than 1 that are only divisible by 1 and themselves.
   
• Sieve of Eratosthenes: An ancient algorithm for finding all prime numbers up to a specified integer.