Is 184 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 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 184 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 184 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 184 is prime or composite.

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

Step 2: Divide 184 by 2. It is divisible by 2, so 2 is a factor of 184.

Step 3: Divide 184 by 3. It is not divisible by 3, so 3 is not a factor of 184.

Step 4: You can simplify checking divisors up to 184 by finding the root value. We then need to only check divisors up to the root value.

Step 5: When we divide 184 by 2, 4, and 8, it is divisible by 2 and 4.

Since 184 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 is 4. Four is an even number, which means that 184 is divisible by 2.

Divisibility by 3: The sum of the digits in the number 184 is 13. Since 13 is not divisible by 3, 184 is also not divisible by 3. 

Divisibility by 5: The unit’s place digit is 4. Therefore, 184 is not divisible by 5.

Divisibility by 7: Use the rule by doubling the last digit (4 × 2 = 8), then subtracting it from the rest of the number (18 - 8 = 10). Since 10 is not divisible by 7, 184 is also not divisible by 7. 

Divisibility by 11: In 184, the difference between the sum of the digits in odd positions and even positions is 5 (1 + 4 - 8 = -3). This would mean that 184 is not divisible by 11.

Since 184 is divisible only by 2 among these, 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 1 to 200 in rows and 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 200. 184 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 184 as 2 × 92.

Step 2: In 2 × 92, 92 is a composite number. Further, break the 92 into 2 × 46.

Step 3: Break 46 into 2 × 23. Now we get the product consisting of only prime numbers.

Hence, the prime factorization of 184 is 2 × 2 × 2 × 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 12 is divisible by 1, 2, 3, 4, 6, and 12.
   
• Prime factorization: The process of breaking down a number into its prime factors. For example, the prime factorization of 28 is 2 × 2 × 7.
   
• Divisibility rules: A set of rules that help determine whether one number is divisible by another without performing division.
   
• Co-prime numbers: Two numbers are co-prime if they have no common factors other than 1. For example, 15 and 28 are co-prime.
   
• Sieve of Eratosthenes: An ancient algorithm used to find all prime numbers up to any given limit.