Is 103 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 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 103 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 103 has only two factors, it is a prime number. A few methods are used to distinguish between prime and composite numbers. Some of them 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 103 is prime or composite.

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

Step 2: Divide 103 by 2. It is not divisible by 2, so 2 is not a factor of 103.

Step 3: Divide 103 by 3. It is not divisible by 3, so 3 is not a factor of 103.

Step 4: You can simplify checking divisors up to 103 by finding the root value. We then need to only check divisors up to the root value.

Step 5: When we divide 103 by numbers up to its square root, it is not divisible by any except 1 and 103. Since 103 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: The number in the ones' place value is 3. Since 3 is not an even number, 103 is not divisible by 2.

Divisibility by 3: The sum of the digits in the number 103 is 4. Since 4 is not divisible by 3, 103 is also not divisible by 3.

Divisibility by 5: The unit’s place digit is 3. Therefore, 103 is not divisible by 5.

Divisibility by 7: The last digit in 103 is 3. To check divisibility by 7, double the last digit (3 × 2 = 6). Then, subtract it from the rest of the number (10 - 6 = 4). Since 4 is not divisible by 7, 103 is also not divisible by 7.

Divisibility by 11: In 103, the sum of the digits in odd positions is 4, and the sum of the digits in even positions is 0. This would mean that 103 is not divisible by 11. Since 103 is only divisible by 1 and 103, 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 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. 103 is not present in the list, but using a similar process beyond 100, we see that 103 is 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. Since 103 is a prime number, it cannot be factored into other prime numbers. The prime factorization of 103 is simply 103 itself.

• Prime numbers: Natural numbers greater than 1 that have no divisors other than 1 and themselves. For example, 103 is a prime number because it is only divisible by 1 and 103.
   
• Composite numbers: Natural numbers greater than 1 that have more than two divisors. For example, 12 is a composite number because it is divisible by 1, 2, 3, 4, 6, and 12.
   
• Divisibility rules: Rules that help determine whether one number is divisible by another without performing division.
   
• Sieve of Eratosthenes: An ancient algorithm used to find all prime numbers up to a specified integer.
   
• Co-prime numbers: Two numbers that have no common factors other than 1. For example, 8 and 15 are co-prime.