Is 489 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 that is 1.
  
   

As 489 has more than two factors, it is not a prime number.

The characteristic of a prime number is that it has only two divisors: 1 and itself.

• Since 489 has more than two factors, it is not 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 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 489 is prime or composite.

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

Step 2: Divide 489 by 2. It is not divisible by 2, as it is an odd number.

Step 3: Divide 489 by 3. The sum of the digits (4 + 8 + 9 = 21) is divisible by 3, so 489 is divisible by 3.

Step 4: You can simplify checking divisors up to 489 by finding the root value. We then need to only check divisors up to the root value.

Step 5: When we divide 489 by 3, it is divisible, giving more factors. Since 489 has more than 2 divisors, it is a composite 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: The number in the ones' place value is 9, which is odd, so 489 is not divisible by 2.

Divisibility by 3: The sum of the digits in the number 489 is 21. Since 21 is divisible by 3, 489 is also divisible by 3.

Divisibility by 5: The unit’s place digit is 9. Therefore, 489 is not divisible by 5.

Divisibility by 7: Double the last digit (9 × 2 = 18) and subtract it from the rest of the number (48 - 18 = 30). Since 30 is divisible by 3, 489 is divisible by 3.

Divisibility by 11: In 489, the alternating sum of the digits is 4 - 8 + 9 = 5, which is not divisible by 11. So, 489 is not divisible by 11.

Since 489 is divisible by more than just 1 and 489, it is a composite 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 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.

Through this process, we will have a list of prime numbers from 1 to 100.
 

The list is 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97.
 

489 is not present in the list of prime numbers, so it is a composite 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: We can write 489 as 3 × 163.
 

Step 2: 163 is a prime number and cannot be factored further. Hence, the prime factorization of 489 is 3 × 163.
 

• Composite numbers: Natural numbers greater than 1 that are divisible by more than 2 numbers are called composite numbers. For example, 12 is a composite number because 12 is divisible by 1, 2, 3, 4, 6, and 12.
   
• Prime numbers: Natural numbers greater than 1 that have no divisors other than 1 and themselves.
   
• Divisibility test: A set of rules to determine if one number is divisible by another without performing full 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.