Is 1493 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:

• 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.
   
• Since 1493 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 1493 has only two factors, it is a prime number. A 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 is prime. 
   
• If the count is more than 2, then the number is composite.

Let’s check whether 1493 is prime or composite.

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

Step 2: Check divisors from 2 up to the square root of 1493 (approximately 38.6).

Step 3: 1493 is not divisible by any integer between 2 and 38.

Since 1493 has only two divisors, 1 and itself, 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: 1493 is an odd number, so it is not divisible by 2. 

Divisibility by 3: The sum of the digits in 1493 is 17, which is not divisible by 3, so 1493 is not divisible by 3. 

Divisibility by 5: 1493 does not end in 0 or 5, so it is not divisible by 5.

Divisibility by 7, 11, etc.: Testing further divisibility rules up to the square root of 1493 confirms it is not divisible by these numbers.

Since 1493 is not divisible by any number other than 1 and itself, it has no divisors other than these, making it 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 starting from 1.

Step 2: Leave 1 without coloring or crossing, as it is neither prime nor composite.

Step 3: Mark 2 as a prime number and cross out all the multiples of 2.

Step 4: Mark 3 as 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, you can identify that 1493 is not crossed out and is thus 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: Start with the smallest prime number, 2. Since 1493 is odd, it’s not divisible by 2.

Step 2: Check divisibility by successive primes (3, 5, 7, etc.) up to the square root of 1493.

Step 3: Since 1493 isn’t divisible by any of these primes, it remains as it is.

The prime factorization of 1493 is 1493 itself.

• Prime Numbers: Natural numbers greater than 1 that are divisible only by 1 and themselves. For example, 5 is a prime number. 
   
• Composite Numbers: Natural numbers greater than 1 that are divisible by more than 2 numbers. For example, 12 is a composite number because it is divisible by 1, 2, 3, 4, 6, and 12. 
   
• Divisibility Rules: Guidelines that help determine if one number is divisible by another without performing full division. For example, a number is divisible by 2 if its last digit is even. 
   
• Sieve of Eratosthenes: An ancient algorithm used to find all primes 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 numbers.