Is 588 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 588 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 588 has more than two factors, it is not a prime number. A 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 588 is prime or composite.

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

Step 2: Divide 588 by 2. It is divisible by 2, so 2 is a factor of 588.

Step 3: Divide 588 by 3. It is divisible by 3, so 3 is a factor of 588.

Step 4: You can simplify checking divisors by finding the square root value. We then need to only check divisors up to the square root value.

Step 5: 588 is divisible by 2, 3, and 4.

Since 588 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 8. Since 8 is an even number, 588 is divisible by 2. 

Divisibility by 3: The sum of the digits in the number 588 is 21. Since 21 is divisible by 3, 588 is also divisible by 3. 

Divisibility by 5: The unit’s place digit is 8. Therefore, 588 is not divisible by 5.

Divisibility by 7: Double the last digit (8 × 2 = 16). Subtract it from the rest of the number (58 - 16 = 42). Since 42 is divisible by 7, 588 is also divisible by 7. 

Divisibility by 11: In 588, the sum of the digits in odd positions is 13, and the sum of the digits in even positions is 8. The difference is 5, which means that 588 is not divisible by 11.

Since 588 is divisible by 2, 3, 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 1000 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 table consisting of marked and crossed boxes, except 1.

Through this process, we will have a list of prime numbers. 588 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 588 as 2 × 294.

Step 2: In 2 × 294, 294 is a composite number. Further, break 294 into 2 × 147.

Step 3: Now break 147 into 3 × 49.

Step 4: Finally, break 49 into 7 × 7.

Hence, the prime factorization of 588 is 2 × 2 × 3 × 7 × 7.

•  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 it is divisible by 1, 2, 3, 4, 6, and 12. 

• Twin primes: The pair of prime numbers whose difference is 2 are called twin prime numbers. For example, (11, 13) is a pair of twin primes because the difference of 13 and 11 is 2.

• 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. 

• Divisibility rules: Simple rules that help determine if one number is divisible by another without performing division. 

• Prime factorization: The process of expressing a number as the product of its prime factors.