Is 1303 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 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 1303 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 1303 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 numbers as prime or 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 1303 is prime or composite.

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

Step 2: Check divisibility by numbers less than the square root of 1303, which is approximately 36.

Step 3: 1303 is not divisible by any number other than 1 and itself.

Since 1303 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: 1303 is not an even number, so it is not divisible by 2.

Divisibility by 3: The sum of the digits in the number 1303 is 7. Since 7 is not divisible by 3, 1303 is not divisible by 3.

Divisibility by 5: The unit’s place digit is 3. Therefore, 1303 is not divisible by 5.

Divisibility by 7: Without a remainder, 1303 is not divisible by 7.

Divisibility by 11: The alternating sum of the digits is not divisible by 11, so 1303 is not divisible by 11.

Since 1303 is not divisible by any number other than 1 and itself, it is a prime number.

The prime number chart is a tool created 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. Since 1303 is greater than 100, you would need an extended chart to include 1303.

Not finding any divisors in this range indicates 1303 is a prime number.

Prime factorization is a process of breaking down a number into prime factors and then multiplying those factors to obtain the original number.

Since 1303 cannot be divided evenly by any prime numbers less than or equal to its square root, we conclude that 1303 is a prime number because it is only divisible by 1 and itself.

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

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

• Divisibility: The ability of one number to be divided by another 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.

• Prime factorization: The process of expressing a number as the product of its prime factors.