Is 188 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 188 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 188 has more than two factors, it is not a prime number. A few methods are used to distinguish between prime and composite numbers. Some 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 and 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 188 is prime or composite.

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

Step 2: Divide 188 by 2. It is divisible by 2, so 2 is a factor of 188.

Step 3: Divide 188 by 3. It is not divisible by 3, so 3 is not a factor of 188.

Step 4: You can simplify checking divisors up to 188 by finding the root value. We then need to only check divisors up to the root value.

Step 5: When we divide 188 by 2, 4, 47, and other numbers, it is divisible by 2 and 4.

Since 188 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 in the ones' place value is 8. Since 8 is an even number, 188 is divisible by 2.

Divisibility by 3: The sum of the digits in the number 188 is 17. Since 17 is not divisible by 3, 188 is also not divisible by 3.

Divisibility by 5: The unit’s place digit is 8. Therefore, 188 is not divisible by 5.

Divisibility by 7: The last digit in 188 is 8. To check divisibility by 7, double the last digit (8 × 2 = 16). Then, subtract it from the rest of the number (18 - 16 = 2). Since 2 is not divisible by 7, 188 is also not divisible by 7.

Divisibility by 11: In 188, the alternating sum of the digits (1 - 8 + 8) is 1. This means that 188 is not divisible by 11.

Since 188 is divisible by more than two numbers, 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 numbers from 1 to 100 (or necessary range) 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 cover the necessary range. Through this process, we will have a list of prime numbers.

Since 188 is not present in the list of prime numbers, 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 188 as 2 × 94.

Step 2: In 2 × 94, 94 is a composite number. Further, break down the 94 into 2 × 47.

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

Hence, the prime factorization of 188 is 2 × 2 × 47.

• 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.
   
• Prime numbers: Numbers greater than 1 that have no divisors other than 1 and themselves. For example, 5 is a prime number.
   
• Divisibility: A number is divisible by another number if the division results in a whole number without a remainder.
   
• Prime factorization: The process of expressing a number as a product of its prime factors. For example, the prime factorization of 18 is 2 × 3 × 3.
   
• Sieve of Eratosthenes: An ancient algorithm to find all prime numbers up to a specified integer.