Is 1189 a Prime Number?

There are two primary types of numbers —

prime numbers and composite numbers, based 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 certain 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 1189 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 1189 has more than two factors, it is not a prime number. Several methods can be used to distinguish between prime and composite numbers. Some of these 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 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 1189 is prime or composite.

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

Step 2: Divide 1189 by 2. It is not divisible by 2, so 2 is not a factor.

Step 3: Divide 1189 by 3. It is not divisible by 3, so 3 is not a factor.

Step 4: Continue this process with other numbers up to the square root of 1189, which is approximately 34.5.

Step 5: When dividing 1189 by 13, it is divisible by 13.

Since 1189 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, which is called the Divisibility Test Method.

Divisibility by 2: The number in the ones' place is 9, which is odd, so 1189 is not divisible by 2. 

Divisibility by 3: The sum of the digits in 1189 is 19. Since 19 is not divisible by 3, 1189 is not divisible by 3. 

Divisibility by 5: The unit’s place digit is 9, so 1189 is not divisible by 5. 

Divisibility by 11: The alternating sum of the digits is (1 - 1 + 8 - 9 = -1), which is not divisible by 11.

Divisibility by 13: When we divide 1189 by 13, it results in a whole number, confirming that 1189 is divisible by 13.

Since 1189 is divisible by 13, it has more than two factors and is a composite number.

The prime number chart is a tool created using a method called “The Sieve of Eratosthenes.” In this method, we follow these 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 multiples of 2.

Step 4: Mark 3 because it is a prime number and cross out all multiples of 3.

Step 5: Repeat this process until you reach the table consisting of marked and crossed boxes, except 1. 1189 is not in the list of prime numbers from 1 to 100.

Since it is divisible by 13, it is a composite number.

Prime factorization is a process of breaking down a number into prime factors, then multiplying those factors to obtain the original number.

Step 1: We can write 1189 as 13 × 91.

Step 2: Further factor 91 into 7 × 13.

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

Hence, the prime factorization of 1189 is 7 × 13 × 13.

• Composite Numbers: Natural numbers greater than 1 that are divisible by more than two numbers are called composite numbers. For example, 12 is a composite number because it is divisible by 1, 2, 3, 4, 6, and 12.
   
• Divisibility: A concept used to determine if one number can be divided by another without leaving a remainder. 
   
• Factors: The numbers that divide the number exactly without leaving a remainder are called factors. For example, the factors of 4 are 1, 2, and 4 because they divide 4 completely. 
   
• Prime Factorization: The process of breaking down a number into its basic prime number components.
   
• Sieve of Eratosthenes: An ancient algorithm used to find all prime numbers up to a specified integer.