Is 8303 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 such as:

• 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.
   
• To determine if 8303 is a prime number, we need to verify if it has only two factors: 1 and 8303 itself.

The characteristic of a prime number is that it has only two divisors: 1 and itself. Since 8303 has more than two factors, it is not a prime number. A few methods are used to identify whether a number is prime or composite, such as:

• Counting Divisors Method
  
   
• Divisibility Test
  
   
• Prime Number Chart
  
   
• Prime Factorization

The counting divisors method involves determining the number of divisors a number has to classify it as prime or composite.

If there are only 2 divisors, the number is prime.

If the count is more than 2, the number is composite.

Let’s check whether 8303 is prime or composite.

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

Step 2: Check divisibility of 8303 by smaller prime numbers like 2, 3, 5, 7, etc.

Step 3: Since 8303 is odd, it is not divisible by 2.

Step 4: Sum of digits of 8303 (8+3+0+3=14) is not divisible by 3, so 8303 is not divisible by 3.

Step 5: The last digit is not 0 or 5, so 8303 is not divisible by 5.

Step 6: Check divisibility by further primes up to the square root of 8303. Since 8303 is divisible by 53 (8303 ÷ 53 = 157), it has more than 2 divisors, so it is a composite number.

We use a set of rules to check whether a number is divisible by another number completely. It is called the Divisibility Test Method.

- Divisibility by 2: 8303 is not even, so it is not divisible by 2.

- Divisibility by 3: The sum of the digits (14) is not divisible by 3.

- Divisibility by 5: The last digit is 3, so it is not divisible by 5.

- Divisibility by 7 and higher primes: Continue testing divisibility by subsequent primes up to the square root of 8303.

Since 8303 is divisible by 53, it is a composite number.

The prime number chart is a tool created using the "Sieve of Eratosthenes." In this method, we follow these steps:

Step 1: Write numbers in a grid format.

Step 2: Identify and mark prime numbers, starting with 2, then 3, etc.

Step 3: Eliminate multiples of each prime number identified.

Step 4: Continue this process up to the desired range. 8303 is not within the range of typical prime charts, and further testing shows it is divisible by 53.

Prime factorization involves breaking down a number into its prime factors.

Step 1: Attempt to divide 8303 by smaller prime numbers.

Step 2: 8303 is divisible by 53, yielding 157.

Step 3: Verify 157 is prime as it is not divisible by any smaller prime numbers.

Thus, the prime factorization of 8303 is 53 × 157.

• Prime numbers: Natural numbers greater than 1 that have no divisors other than 1 and themselves.
  
   
• Composite numbers: Natural numbers greater than 1 that have more than two divisors.
  
   
• Divisibility rules: Guidelines for determining if a number can be divided by another without a remainder.
  
   
• Prime factorization: Expressing a number as a product of its prime factors.
  
   
• Sieve of Eratosthenes: An ancient algorithm for finding all prime numbers up to a specified integer.