Is 574 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 574 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 574 has more than two factors, it is not a prime number. A few methods are used to distinguish between prime and composite numbers. Some 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 574 is prime or composite.

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

Step 2: Divide 574 by 2. It is divisible by 2, so 2 is a factor of 574.

Step 3: Divide 574 by 3. It is not divisible by 3, so 3 is not a factor of 574.

Step 4: You can simplify checking divisors up to 574 by finding the root value. We then need to only check divisors up to the root value. Step 5: When we divide 574 by 2, we find it is divisible by 2.

Since 574 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 value is 4. Four is an even number, which means that 574 is divisible by 2.

Divisibility by 3: The sum of the digits in the number 574 is 16. Since 16 is not divisible by 3, 574 is also not divisible by 3.

Divisibility by 5: The unit’s place digit is 4. Therefore, 574 is not divisible by 5.

Divisibility by 7: To check divisibility by 7, double the last digit (4 × 2 = 8). Then, subtract it from the rest of the number (57 - 8 = 49). Since 49 is divisible by 7, 574 is also divisible by 7.

Divisibility by 11: In 574, alternating sums of the digits are 5 - 7 + 4 = 2. Since 2 is not divisible by 11, neither is 574. Since 574 is divisible by 2 and 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 up to a certain limit 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 point where the table is finalized with marked and crossed boxes, except 1. Through this process, we will have a list of prime numbers.

574 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 574 as 2 × 287.

Step 2: In 2 × 287, 287 is a composite number. Further, break 287 into 7 × 41.

Step 3: Now we get the product consisting of only prime numbers.

Hence, the prime factorization of 574 is 2 × 7 × 41.

• 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. Examples include 2, 3, 5, 7, etc.
  
   
• Factors: The numbers that divide the number exactly without leaving a remainder are called factors. For example, the factors of 8 are 1, 2, 4, and 8 because they divide 8 completely.
  
   
• Divisibility: A characteristic of integers which can be divided by another integer without leaving a remainder.
  
   
• Prime factorization: The process of expressing a number as the product of its prime factors. For example, the prime factorization of 18 is 2 × 3 × 3.