Is 586 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 586 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 586 has more than two factors, it is not 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 586 is prime or composite.

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

Step 2: Divide 586 by 2. It is divisible by 2, so 2 is a factor of 586.

Step 3: Divide 586 by 3. It is not divisible by 3, so 3 is not a factor of 586.

Step 4: You can simplify checking divisors up to 586 by finding the root value. We then need to only check divisors up to the root value.

Step 5: When we divide 586 by 2, 3, 11, and 29, it is divisible by 2, 11, and 29.

Since 586 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 one's place value is 6. Since 6 is an even number, 586 is divisible by 2.

Divisibility by 3: The sum of the digits in the number 586 is 19. Since 19 is not divisible by 3, 586 is also not divisible by 3.

Divisibility by 5: The unit’s place digit is 6. Therefore, 586 is not divisible by 5.

Divisibility by 7: Using the rule for 7, 586 is not divisible by 7.

Divisibility by 11: The alternating sum of the digits is 5 - 8 + 6 = 3, which is not divisible by 11.

Divisibility by 13: Using the rule for 13, 586 is not divisible by 13.

Since 586 is divisible by more than 2 numbers, 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 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.

The list includes numbers such as 2, 3, 5, 7, 11, 13, etc. 586 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 its prime factors. Then multiply those factors to obtain the original number.

Step 1: We can write 586 as 2 × 293.

Step 2: In 2 × 293, both numbers are prime, so no further breakdown is needed.

Therefore, the prime factorization of 586 is 2 × 293.

• 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 factorization: The process of expressing a number as the product of its prime factors.

• Divisibility rules: Shortcuts or rules to quickly determine if a number is divisible by another number without performing long division.

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

• Co-prime numbers: Two numbers are co-prime if their greatest common divisor is 1.