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 151 has only two factors, it is a prime number.

The characteristic of a prime number is that it has only two divisors: 1 and itself. Since 151 has only two factors, it is a prime number. 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 151 is prime or composite.

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

Step 2: Check divisibility of 151 by numbers up to the square root of 151 (approximately 12.3).

Step 3: 151 is not divisible by 2, 3, 5, 7, or 11 since it does not result in a whole number.

Since 151 has only 2 divisors, it is a prime 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: 151 is not divisible by 2 as it is not even.

Divisibility by 3: The sum of the digits in the number 151 is 7. Since 7 is not divisible by 3, 151 is also not divisible by 3.

Divisibility by 5: The unit’s place digit is 1. Therefore, 151 is not divisible by 5.

Divisibility by 7 and 11: Performing calculations show that 151 is not divisible by either.

Since 151 is not divisible by any numbers other than 1 and itself, it confirms that it is a prime 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 several 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. 151 is present in the list of prime numbers, confirming it as a prime 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: Consider 151 and attempt to divide by prime numbers like 2, 3, 5, 7, and 11.

Step 2: None of these divisions result in a whole number factorization.

Since 151 cannot be broken down into other prime factors beyond 1 and itself, it is a prime number.

• Prime numbers: Natural numbers greater than 1 that have no divisors other than 1 and itself. For example, 5 is a prime number.

• Composite numbers: Natural numbers greater than 1 that have more than two factors. For example, 12 is a composite number.

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

• Divisibility rules: Guidelines that help to determine whether one number is divisible by another.

• Sieve of Eratosthenes: An ancient algorithm used to find all prime numbers up to a specified integer.