Is 589 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 589 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 589 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 numbers as either 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 589 is prime or composite.

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

Step 2: Divide 589 by 2. It is not divisible by 2.

Step 3: Divide 589 by 3. It is not divisible by 3.

Step 4: You can simplify checking divisors up to 589 by finding the root value. We then need to only check divisors up to the root value.

Step 5: When we divide 589 by 13, it is divisible by 13 and 45.38.

Since 589 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 an odd number, so 589 is not divisible by 2. 

Divisibility by 3: The sum of the digits in the number 589 is 22. Since 22 is not divisible by 3, 589 is also not divisible by 3. 

Divisibility by 5: The unit’s place digit is 9. Therefore, 589 is not divisible by 5.

Divisibility by 13: When 589 is divided by 13, it is divisible, as 589 ÷ 13 = 45.38, which means it is not divisible. 

Divisibility by 19: The last digit in 589 is 9. To check divisibility by 19, subtract the last digit from twice the rest of the number (58 - 2*9 = 40).

Since 40 is not divisible by 19, 589 is also not divisible by 19. Since 589 is divisible by more than one number, it has more than two factors. Therefore, 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 a range of numbers, such as 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 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. 589 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 initially divide 589 by 19, which gives 31.

Step 2: Now, we have 19 × 31, both of which are prime numbers.

Step 3: Hence, the prime factorization of 589 is 19 × 31.

• 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: Numbers greater than 1 that are divisible only by 1 and themselves.

• Divisibility rules: Guidelines that help determine whether one number is divisible by another without performing division.

• Factorization: The process of breaking down a number into its prime factors.

• Sieve of Eratosthenes: An ancient algorithm used to find all prime numbers up to a specified integer.