Is 1194 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 1194 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 1194 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 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 1194 is prime or composite.

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

Step 2: Divide 1194 by 2. It is divisible by 2, so 2 is a factor of 1194.

Step 3: Divide 1194 by 3. It is divisible by 3, so 3 is a factor of 1194.

Step 4: You can simplify checking divisors up to 1194 by finding the root value. We then need to only check divisors up to the root value.

Step 5: When we divide 1194 by other numbers, it is also divisible by 6, 9, and 18.

Since 1194 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: 1194 ends in 4, which is an even number, so it is divisible by 2.

Divisibility by 3: The sum of the digits in the number 1194 is 15. Since 15 is divisible by 3, 1194 is divisible by 3. 

Divisibility by 5: The unit’s place digit is 4. Therefore, 1194 is not divisible by 5.

Divisibility by 7: Using the divisibility rule for 7, 1194 divided by 7 equals 170.57, which is not an integer, so it is not divisible by 7. 

Divisibility by 11: For 1194, the difference between the sum of digits in odd positions (1 + 9) and even positions (1 + 4) is 5, which is not divisible by 11. Thus, 1194 is not divisible by 11.

Since 1194 is divisible by 2, 3, and other numbers, it has more than two factors. Therefore, it is a composite number.

A prime number chart is a tool created using a method called “The Sieve of Eratosthenes.” In this method, we follow the steps below:

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, such as 2, 3, 5, 7, etc.

Since 1194 is not present in the list of prime numbers and is greater than 100, 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 1194 as 2 × 597.

Step 2: In 2 × 597, 597 is a composite number. Further, break 597 into 3 × 199.

Step 3: 199 is a prime number; hence, the prime factorization of 1194 is 2 × 3 × 199.

• Composite Numbers: Natural numbers greater than 1 that are divisible by more than 2 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 Rules: A set of rules that help 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. 
   
• Co-prime Numbers: Two numbers that have no common factors other than 1. 
   
• Perfect Square: A number that can be expressed as the product of an integer with itself.