Is 518 a Prime Number?

There are two types of numbers, mainly —

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 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 518 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 518 has more than two factors, it is not a prime number.

Several methods are used to distinguish between prime and composite numbers.

Some of these methods include:

• 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 or 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 518 is prime or composite.

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

Step 2: Divide 518 by 2. It is divisible by 2, so 2 is a factor of 518.

Step 3: Divide 518 by 3. It is not divisible by 3, so 3 is not a factor of 518.

Step 4: Simplify checking divisors up to 518 by finding the square root value. We then need to only check divisors up to the square root value.

Since 518 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, 518 is divisible by 2.

Divisibility by 3: The sum of the digits in the number 518 is 14. Since 14 is not divisible by 3, 518 is also not divisible by 3.

Divisibility by 5: The unit’s place digit is 8. Since 8 does not end in 0 or 5, 518 is not divisible by 5.

Divisibility by 7: Using the rule for 7, we find that 518 is not divisible by 7.

Divisibility by 11: Applying the divisibility rule for 11, 518 is not divisible by 11.

Since 518 is divisible by 2, 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 steps below:

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 for subsequent numbers until all prime numbers are identified. Through this process, we will have a list of prime numbers.

518 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 518 as 2 × 259.

Step 2: In 2 × 259, 259 is a composite number. Further, break the 259 into 7 × 37.

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

Hence, the prime factorization of 518 is 2 × 7 × 37.

• 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.

• Prime factorization: The process of breaking down a number into a product of prime numbers. For example, the prime factorization of 30 is 2 × 3 × 5.

• Divisibility rules: Rules that help determine if one number is divisible by another without performing division. For example, a number is divisible by 3 if the sum of its digits is divisible by 3.

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

• Sieve of Eratosthenes: An ancient algorithm used to find all prime numbers up to a specified integer by systematically marking the multiples of each prime number starting from 2.