Is 1186 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, such as:

• 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 1186 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 1186 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 1186 is prime or composite.

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

Step 2: Divide 1186 by 2. It is divisible by 2, so 2 is a factor of 1186.

Step 3: Divide 1186 by 3. It is not divisible by 3, so 3 is not a factor of 1186.

Step 4: You can simplify checking divisors up to 1186 by finding the square root value. We then need to only check divisors up to the square root value.

Since 1186 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: The number in the ones' place value is 6, which is an even number. Therefore, 1186 is divisible by 2.

Divisibility by 3: The sum of the digits in the number 1186 is 16. Since 16 is not divisible by 3, 1186 is also not divisible by 3.

Divisibility by 5: The unit’s place digit is not 0 or 5. Therefore, 1186 is not divisible by 5.

Divisibility by 7: To check divisibility by 7, double the last digit (6 × 2 = 12). Subtract it from the rest of the number (118 - 12 = 106). Since 106 is not divisible by 7, 1186 is also not divisible by 7. 

Divisibility by 11: In 1186, the sum of the digits in odd positions is 1 + 8 = 9, and the sum of the digits in even positions is 1 + 6 = 7. The difference is 9 - 7 = 2, which is not divisible by 11. Therefore, 1186 is not divisible by 11.

Since 1186 is divisible by 2, 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 in sequential order.

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 have a table consisting of marked and crossed boxes, except 1. Through this process, we will have a list of prime numbers.

1186 is not present 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 write 1186 as 2 × 593.

Step 2: Check if 593 is a composite number. It is not, as 593 is a prime number.

Therefore, the prime factorization of 1186 is 2 × 593.

• 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 divisors.
   
• Factors: Numbers that divide another number exactly without leaving a remainder.
   
• Divisibility Rules: Guidelines to determine whether one number is divisible by another without performing division.
   
• Prime Factorization: The process of expressing a number as the product of its prime factors.