Is 581 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.
   
• As 581 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 581 has more than two factors, it is not a prime number. A few methods are used to distinguish between prime and composite numbers:

• 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 581 is prime or composite.

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

Step 2: Divide 581 by 2. It is not divisible by 2.

Step 3: Divide 581 by 3. The sum of the digits (5 + 8 + 1 = 14) is not divisible by 3.

Step 4: Divide 581 by 7. It is divisible by 7, so 7 is a factor of 581.

Since 581 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 is 1. Since 1 is not even, 581 is not divisible by 2.

Divisibility by 3: The sum of the digits in the number 581 is 14. Since 14 is not divisible by 3, 581 is also not divisible by 3.

Divisibility by 5: The unit’s place digit is 1. Therefore, 581 is not divisible by 5.

Divisibility by 7: Divide 581 by 7, which gives a whole number (83), so 581 is divisible by 7.

Since 581 is divisible by 7, 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 numbers in a sequence.

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 for other prime numbers. Through this process, we will have a list of prime numbers.

Since 581 is divisible by 7, it 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 581 as 7 × 83.

Step 2: Both 7 and 83 are prime numbers.

Hence, the prime factorization of 581 is 7 × 83.

• 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 itself. For example, 5 is a prime number because it is divisible only by 1 and 5.
   
• Divisibility: A number is divisible by another if it can be divided without leaving a remainder.
   
• Factors: The numbers that divide the number exactly without leaving a remainder are called factors. For example, the factors of 4 are 1, 2, and 4 because they divide 4 completely.
   
• Prime Factorization: The process of expressing a number as a product of its prime factors. For example, the prime factorization of 20 is 2 × 2 × 5.