Is 1363 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 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 1363 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 1363 has only two factors, it is a prime number. Several 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 1363 is prime or composite.

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

Step 2: Check divisibility by numbers up to the square root of 1363, which is approximately 36.9.

Step 3: Verify divisibility by prime numbers like 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37.

Since 1363 is not divisible by any of these, it remains with only 1 and 1363 as its factors, confirming it as 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: 1363 is odd, so it's not divisible by 2.

Divisibility by 3: The sum of the digits in the number 1363 is 13, which is not divisible by 3.

Divisibility by 5: The unit’s place digit is 3, so 1363 is not divisible by 5.

Check divisibility by other primes up to around 37: None divide 1363 without a remainder

Since 1363 is not divisible by any smaller prime numbers, it confirms 1363 is prime.

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 manageable range, e.g., from 1 to 1000 or 100 to 2000, in 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.

Since 1363 is not crossed out by any step, it remains marked 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: Attempt to divide 1363 by smaller prime numbers.

Step 2: Verify that no smaller prime numbers divide 1363 completely, leaving no remainder.

Step 3: Since no prime factors divide 1363 other than itself and 1, 1363 remains prime.

• 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: A number is divisible by another if it can be divided without leaving a remainder.
  
   
• Prime factorization: Expressing a number as a product of its prime factors.
  
   
• Sieve of Eratosthenes: An ancient algorithm used to find all primes up to a specified integer.