Is 1173 a Prime Number?

There are two main types of numbers —

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 1173 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 1173 has more than two factors, it is not a prime number.

Several methods are used to distinguish between prime and composite numbers.

These methods include:

• Counting Divisors Method 
   
• Divisibility Test 
   
• Prime Number Chart 
   
• Prime Factorization

The counting divisors method involves counting the number of divisors to categorize numbers as prime or composite. Based on the count of the divisors, we categorize numbers accordingly.

• 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 1173 is prime or composite.

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

Step 2: Divide 1173 by 2. It is not divisible by 2, so 2 is not a factor of 1173.

Step 3: Divide 1173 by 3. It is divisible by 3, so 3 is a factor of 1173.

Step 4: You can simplify checking divisors up to 1173 by finding the square root value. We then need to only check divisors up to the square root value.

Since 1173 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. This is called the Divisibility Test Method. 

Divisibility by 2: The number 1173 is odd, so it is not divisible by 2. 

Divisibility by 3: The sum of the digits in 1173 is 12 (1+1+7+3), which is divisible by 3. Therefore, 1173 is divisible by 3. 

Divisibility by 5: The unit’s place digit is 3. Therefore, 1173 is not divisible by 5. 

Divisibility by 7: Use the rule of doubling the last digit and subtracting it from the rest of the number. Doubling 3 gives 6, and subtracting it from 117 gives 111, which is divisible by 7. Therefore, 1173 is divisible by 7. 

Divisibility by 11: The difference between the sum of digits in odd positions and the sum of digits in even positions is 0, which is divisible by 11.

Since 1173 is divisible by numbers other than 1 and itself, it has more than two factors, making it a composite number.

The prime number chart is a tool created by a method called “The Sieve of Eratosthenes.” In this method, we follow these steps:

Step 1: Write numbers 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. Through this process, we will have a list of prime numbers from 1 to 100.

Since 1173 is not part of this list and has factors other than 1 and itself, it is a composite number.

Prime factorization involves breaking down a number into its prime factors and then multiplying those factors to obtain the original number.

Step 1: We can write 1173 as 3 × 391.

Step 2: In 3 × 391, 391 is a composite number. Further, break down 391 into 17 × 23.

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

Hence, the prime factorization of 1173 is 3 × 17 × 23.

• 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 guidelines to determine if one number is divisible by another without performing division.

• Factors: Numbers that divide a given number exactly without leaving a remainder. For example, the factors of 4 are 1, 2, and 4.

• Prime factorization: Breaking down a number into its prime factors. For example, the prime factorization of 20 is 2 × 2 × 5.

• Sieve of Eratosthenes: An ancient algorithm for finding all prime numbers up to any given limit.