Is 299 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, 9 is divisible by 1, 3, and 9, 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 299 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 299 has more than two factors, it is not a prime number. A few methods are used to distinguish between prime and composite numbers. 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 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 299 is prime or composite. Step 1: All numbers are divisible by 1 and itself. Step 2: Divide 299 by 2. It is not divisible, so 2 is not a factor. Step 3: Divide 299 by 3. It is not divisible, so 3 is not a factor. Step 4: Divide 299 by 13. It is divisible by 13, so 13 is a factor of 299. Since 299 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 one's place value is 9. Since 9 is not even, 299 is not divisible by 2.

Divisibility by 3: The sum of the digits in the number 299 is 20. Since 20 is not divisible by 3, 299 is also not divisible by 3.

Divisibility by 5: The unit’s place digit is 9. Therefore, 299 is not divisible by 5.

Divisibility by 7: The last digit in 299 is 9. To check divisibility by 7, double the last digit (9 × 2 = 18). Then, subtract it from the rest of the number (29 - 18 = 11). Since 11 is not divisible by 7, 299 is not divisible by 7.

Divisibility by 13: Divide 299 by 13, which results in 23. Therefore, 299 is divisible by 13.

Since 299 is divisible by 13, 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. 299 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 299 as 13 × 23.

Step 2: Both 13 and 23 are prime numbers.

The prime factorization of 299 is 13 × 23.

• 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 are divisible by only 1 and itself. For example, 5 is a prime number because it is divisible by only 1 and 5.
   
• Divisibility Rules: Set of 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.
   
• Co-prime numbers: Two numbers that have only one common factor, which is 1, are called co-prime numbers. For example, 8 and 15 are co-prime numbers.