Is 573 a Prime Number?

There are two main types of numbers: prime numbers and composite numbers, distinguished by the number of factors they have.

A prime number is a natural number that is divisible only by 1 and itself.

For instance, 5 is a prime number because it is divisible by 1 and 5 only.

A composite number is a positive number that is divisible by more than two numbers.

For example, 8 is divisible by 1, 2, 4, and 8, making it a composite number.

Prime numbers have certain properties: 

• Prime numbers are positive integers 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 because they have only one common factor, which is 1.
   
• Since 573 has more than two factors, it is not a prime number.

A prime number is characterized by having only two divisors: 1 and itself. Since 573 has more than two factors, it is not a prime number. There are several methods to distinguish between prime and composite numbers, including: 

• 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 divisors, numbers are classified as follows: - If there is a total count of only 2 divisors, the number is prime.  If the count is more than 2, the number is composite. Let’s check whether 573 is prime or composite: 

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

Step 2: Divide 573 by 2. It is not divisible by 2 since it is odd. 

Step 3: Divide 573 by 3. The sum of the digits (5 + 7 + 3 = 15) is divisible by 3, so 573 is divisible by 3, making 3 a factor. 

Step 4: Simplify checking divisors up to the square root of 573, which is approximately 23.9, so check divisors up to 23. 

Step 5: When we divide 573 by 3, 191 is left, which is not divisible by any number between 2 and 13.

Since 573 has more than 2 divisors, it is a composite number.

A set of rules is used to check whether a number is divisible by another number completely, known as the Divisibility Test Method. 

Divisibility by 2: The number 573 is odd, so it is not divisible by 2. 

Divisibility by 3: The sum of the digits is 15, which is divisible by 3, so 573 is divisible by 3.

 Divisibility by 5: The unit’s place digit is 3, so 573 is not divisible by 5. 

Divisibility by 7: Using the rule, 573 is not divisible by 7. 

Divisibility by 11: Alternating sum = 5 - 7 + 3 = 1, which is not divisible by 11.

Since 573 is divisible by 3, it has more than two factors, and thus is a composite number.

The prime number chart is a tool created using “The Sieve of Eratosthenes.” The steps are: 

Step 1: Write numbers 1 to 100 in rows and columns.

Step 2: Leave 1 without marking, as it is neither prime nor composite.

Step 3: Mark 2 as prime and cross out all multiples of 2. 

Step 4: Mark 3 as prime and cross out all multiples of 3.

Step 5: Continue this process through the list.

The list of prime numbers up to 100 does not include 573. Thus, 573 is a composite number.

Prime factorization involves breaking down a number into its prime factors. Multiply these factors to obtain the original number. 

Step 1: Write 573 as 3 × 191. 

Step 2: 191 is a prime number.

Therefore, the prime factorization of 573 is 3 × 191.

•  Composite numbers: Natural numbers greater than 1 that are divisible by more than 2 numbers. For example, 573 is composite as it is divisible by 1, 3, 191, and 573. 

• Prime numbers: Natural numbers greater than 1 with exactly 2 distinct positive divisors, 1 and themselves. For example, 3 is a prime number. 

• Divisibility: A number's ability to be divided by another number without leaving a remainder. For example, 573 is divisible by 3. 

• Prime factorization: Expressing a number as the product of prime numbers. The prime factorization of 573 is 3 × 191. 

• Co-prime numbers: Two numbers with no common factors other than 1. For example, 8 and 15 are co-prime.