Is 508 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 508 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 508 has more than two factors, it is not a prime number. Several 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 numbers as prime and composite. - 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 508 is prime or composite.

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

Step 2: Divide 508 by 2. It is divisible by 2, so 2 is a factor of 508.

Step 3: Divide 508 by 3. It is not divisible by 3, so 3 is not a factor of 508.

Step 4: You can simplify checking divisors up to 508 by finding the square root value. We then need to only check divisors up to the square root value.

Step 5: When we divide 508 by 2, 4, 127, and other numbers, it is divisible by 2 and 127.

Since 508 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, which is even. Therefore, 508 is divisible by 2. 

Divisibility by 3: The sum of the digits in the number 508 is 13. Since 13 is not divisible by 3, 508 is also not divisible by 3.

Divisibility by 5: The unit’s place digit is 8. Therefore, 508 is not divisible by 5.

Divisibility by 7: The last digit in 508 is 8. Double the last digit (8 × 2 = 16), then subtract it from the rest of the number (50 - 16 = 34). Since 34 is not divisible by 7, 508 is not divisible by 7. 

Divisibility by 11: In 508, the difference between the sum of the digits in odd positions (5 + 8) and the sum of the digits in even positions (0) is 13. Since 13 is not divisible by 11, 508 is also not divisible by 11.

Since 508 is divisible only by 2 and 127, 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 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.

508 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 multiplying those factors to obtain the original number.

Step 1: We can write 508 as 2 × 254.

Step 2: In 2 × 254, 254 is a composite number. Further, break the 254 into 2 × 127.

Step 3: Now we get the product consisting of only prime numbers. Hence, the prime factorization of 508 is 2 × 2 × 127.

• 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.

• Sieve of Eratosthenes: An ancient algorithm used to find all prime numbers up to a specified integer.

• Prime factorization: The process of determining the prime numbers that multiply together to give a specific integer.

• Divisibility rules: A set of rules that help determine if a number is divisible by another without performing division.

• Co-prime numbers: Two numbers that have only 1 as their common factor. For example, 8 and 15 are co-prime.