Is 557 a Prime Number?

There are two types of numbers, mostly

• Prime numbers
   
• 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. Since 557 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 557 has exactly two factors, it is 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 557 is prime or composite.

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

Step 2: Divide 557 by numbers up to its square root (approximately 23.6).

Step 3: Check divisibility by numbers like 2, 3, 5, 7, 11, 13, 17, 19, 23. Since 557 is not divisible by any of these numbers, it has only two divisors: 1 and 557. Hence, 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.

Divisibility by 2: 557 is odd, so it is not divisible by 2.

Divisibility by 3: The sum of the digits of 557 is 17, which is not divisible by 3.

Divisibility by 5: The unit’s place digit is 7, so it is not divisible by 5.

Divisibility by 7: Doubling the last digit and subtracting from the rest gives a result that is not divisible by 7.

Divisibility by 11: Alternating sum of digits gives 7, which is not divisible by 11.

Since 557 is not divisible by any number other than 1 and 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 a limit, say 600, in rows.

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: Continue this process for prime numbers like 5, 7, 11, etc. Through this process, we will have a list of prime numbers up to the chosen limit. 557 is present in the list of prime numbers, confirming it is a prime number.

Prime factorization is a process of breaking down a number into prime factors. Then multiply those factors to obtain the original number. Since 557 is not divisible by any prime numbers up to its square root, it remains as itself, confirming that 557 is a prime number.

• Prime numbers: Numbers greater than 1 that have no divisors other than 1 and themselves.
   
• Composite numbers: Natural numbers greater than 1 that are divisible by more than two numbers.
   
• Divisibility rules: Guidelines that help determine if one number is divisible by another without performing division.
   
• Square root: A number that, when multiplied by itself, gives the original number. Used to simplify factorization.
   
• Sieve of Eratosthenes: An ancient algorithm used to find all prime numbers up to a specified integer.