Is 101 a Prime Number?

There are two types of numbers, mostly

• Prime numbers
   
• 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 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. Since 101 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 101 has exactly 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 101 is prime or composite.

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

Step 2: Check divisibility up to the square root of 101, which is approximately 10.

Step 3: 101 is not divisible by any number other than 1 and itself (2 to 10). Since 101 has exactly 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: 101 is not even, so it is not divisible by 2.

Divisibility by 3: The sum of the digits in the number 101 is 2, which is not divisible by 3.

Divisibility by 5: The unit’s place digit is not 0 or 5, so 101 is not divisible by 5.

Divisibility by 7: Using divisibility rules for 7, 101 cannot be divided evenly by 7.

Divisibility by 11: The alternating sum of the digits is 0, which is not divisible by 11. Since 101 is not divisible by any number other than 1 and itself, 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 numbers in a range, e.g., 1 to 100.

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. 101, though above 100, is known to be prime as it is not divisible by any number other than 1 and itself.

Prime factorization is a process of breaking down a number into prime factors. Then multiply those factors to obtain the original number. Since 101 is a prime number, it cannot be factored further into other prime numbers. It has no factors other than 1 and 101 itself.

• Prime numbers: Natural numbers greater than 1 that have no divisors other than 1 and themselves. For example, 11 is a prime number.
   
• Composite numbers: Natural numbers greater than 1 that are divisible by more than two numbers. For example, 12 is a composite number.
   
• Divisibility: A number's ability to be divided by another number without leaving a remainder. For example, 10 is divisible by 2.
   
• Sieve of Eratosthenes: An ancient algorithm used to find all prime numbers up to a specified integer.
   
• Co-prime numbers: Two numbers that have only 1 as a common factor. For example, 9 and 28 are co-prime numbers. ```