Is 559 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 559 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 559 has more than two factors, it is not a prime number. Several methods are used to distinguish between prime and composite numbers, such as:

• Counting Divisors Method
   
• Divisibility Test
   
• Prime Number Chart
   
• Prime Factorization

The counting divisors method involves counting the number of divisors to categorize numbers as prime or composite. 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 is prime. - If the count is more than 2, then the number is composite. Let’s check whether 559 is prime or composite.
 

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

Step 2: Divide 559 by 2. It is not divisible by 2, so 2 is not a factor of 559.

Step 3: Divide 559 by 3. The sum of the digits (5 + 5 + 9 = 19) is not divisible by 3, so 3 is not a factor of 559.

Step 4: Simplify checking divisors up to the square root of 559, which is approximately 23.6. We check divisors up to 23. Step 5: When we divide 559 by 13, it is divisible, so 13 is a factor of 559, along with 43 (since 559 ÷ 13 = 43).

Since 559 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. This is called the Divisibility Test Method.

Divisibility by 2: 559 is odd, so it is not divisible by 2.

Divisibility by 3: The sum of the digits is 19, which is not divisible by 3.

Divisibility by 5: The unit's place digit is 9, so 559 is not divisible by 5.

Divisibility by 11: The difference between the sum of the digits in odd positions and even positions is 1, which is not divisible by 11.

Divisibility by 13: Upon division, 559 is exactly divisible by 13.

Since 559 is divisible by numbers other than 1 and itself, it has more than two factors. Therefore, it is a composite number.

The prime number chart is a tool created using the method called “The Sieve of Eratosthenes.” In this method, we follow the following steps:

Step 1: Write numbers from 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. 559 is not present in the list of prime numbers, as it is a composite number.

Prime factorization is a process of breaking down a number into prime factors and then multiplying those factors to obtain the original number.

Step 1: We can write 559 as 13 × 43.

Step 2: Both 13 and 43 are prime numbers.

Hence, the prime factorization of 559 is 13 × 43.

• Composite numbers: Natural numbers greater than 1 that are divisible by more than 2 numbers. For example, 12 is a composite number because it is divisible by 1, 2, 3, 4, 6, and 12.
   
• Prime factorization: The expression of a number as the product of its prime factors. For example, the prime factorization of 60 is 2 × 2 × 3 × 5.
   
• Divisibility rules: Set of guidelines to determine if a number is divisible by another without performing division.
   
• Factors: Numbers that divide another number exactly without leaving a remainder. For example, the factors of 4 are 1, 2, and 4.
   
• Sieve of Eratosthenes: An ancient algorithm used to find all prime numbers up to a specified integer.