Is 186 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 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 that is 1.
   
• As 186 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 186 has more than two factors, it is not a prime number. A few 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 186 is prime or composite.

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

Step 2: Divide 186 by 2. It is divisible by 2, so 2 is a factor of 186.

Step 3: Divide 186 by 3. The sum of the digits is 15 (1 + 8 + 6), which is divisible by 3, so 3 is a factor of 186.

Step 4: You can simplify checking divisors by finding the root value of 186 and then checking divisors up to the root value.

Step 5: When we divide 186 by 2, 3, and other numbers, it has multiple divisors.

Since 186 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 6, which is even, so 186 is divisible by 2. 

Divisibility by 3: The sum of the digits in 186 is 15. Since 15 is divisible by 3, so is 186. 

Divisibility by 5: The unit’s place digit is 6. Therefore, 186 is not divisible by 5.

Divisibility by 7: To check divisibility by 7, double the last digit (6 × 2 = 12). Then, subtract it from the rest of the number (18 - 12 = 6). Since 6 is not divisible by 7, 186 is also not divisible by 7. 

Divisibility by 11: In 186, the sum of the digits in odd positions is 7, and the sum of the digits in even positions is 8. The difference is 1, so 186 is not divisible by 11.

Since 186 is divisible by 2 and 3, among others, 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 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.

The list is 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97. 186 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 multiplying those factors to obtain the original number.

Step 1: We can write 186 as 2 × 93.

Step 2: In 93, which is a composite number, further break it down into 3 × 31.

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

Hence, the prime factorization of 186 is 2 × 3 × 31.

• 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 numbers: Natural numbers greater than 1 that have no divisors other than 1 and itself. For example, 13 is a prime number because it is divisible by only 1 and 13.
   
• 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.
   
• Divisibility: A number is divisible by another number if, upon division, the remainder is zero. For example, 20 is divisible by 5 because 20 ÷ 5 = 4 with no remainder.
   
• Prime factorization: The process of expressing a number as the product of its prime factors. For example, the prime factorization of 18 is 2 × 3 × 3.