Is 1489 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 1489 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 1489 has exactly 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 1489 is prime or composite. 

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

Step 2: Divide 1489 by numbers starting from 2 up to its square root (~38.6). It is not divisible by any of these numbers.

Since 1489 has only 2 divisors, 1 and 1489, 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. For 1489: 

Divisibility by 2: 1489 is an odd number, so it is not divisible by 2. 

Divisibility by 3: The sum of the digits in 1489 is 22, which is not divisible by 3. 

Divisibility by 5: The unit’s place digit is 9, so it is not divisible by 5. 

Divisibility by 7: Using the divisibility rule for 7, 1489 is not divisible. 

Divisibility by 11: The difference between the sum of the digits in odd positions and the sum in even positions is not divisible by 11.

Since 1489 is not divisible by any number other than 1 and 1489 itself, 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 numbers from 1 to 1000 in rows and columns.

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

Step 3: Mark the smallest number greater than 1, and cross out all its multiples. 

Step 4: Repeat this process for the next smallest unmarked number.

Through this process, we can verify that 1489 is a prime number because it is only divisible by 1 and itself.

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

Step 1: Attempt to divide 1489 by the smallest prime numbers. 

Step 2: As 1489 is not divisible by any numbers other than 1 and 1489 itself, it cannot be broken down further into other prime factors.

Hence, 1489 is a prime number.

• Prime numbers: Natural numbers greater than 1 that have only two divisors, 1 and the number itself, are called prime numbers. For example, 17 is a prime number because it is only divisible by 1 and 17.
   
• Composite numbers: Natural numbers greater than 1 that are divisible by more than two numbers are called composite numbers. For example, 12 is a composite number because it is divisible by 1, 2, 3, 4, 6, and 12.
   
• Divisibility rules: Set of rules that help determine whether one number is divisible by another without performing the actual division.
   
• Prime factorization: The process of expressing a number as the product of its prime factors.
   
• Sieve of Eratosthenes: An ancient algorithm used to find all prime numbers up to a specified integer.