Is 239 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 239 has only two factors, it is a prime number.

The characteristic of a prime number is that it has only two divisors: 1 and itself. Since 239 has exactly two factors, it is 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 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 239 is prime or composite.

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

Step 2: Divide 239 by 2, 3, 4, 5, ..., up to the square root of 239, which is approximately 15.5.

Step 3: Since 239 is not divisible by any number other than 1 and itself, it is a prime 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 9, which is odd, so 239 is not divisible by 2.

Divisibility by 3: The sum of the digits in the number 239 is 14. Since 14 is not divisible by 3, 239 is also not divisible by 3.

Divisibility by 5: The unit’s place digit is 9. Therefore, 239 is not divisible by 5.

Divisibility by 7: Use the divisibility rule for 7 and find that 239 is not divisible by 7. Continue with other primes up to 15. Since 239 is not divisible by any of these primes, it has no factors other than 1 and 239, confirming it is a prime 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 includes 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. Since 239 is greater than 100, we verify using the earlier methods, confirming it is a prime number.

Prime factorization is a process of breaking down a number into prime factors. Then multiply those factors to obtain the original number. Since 239 is a prime number, it cannot be factored into other primes. Therefore, the prime factorization of 239 is simply 239 itself.

• Prime numbers: Natural numbers greater than 1 that have no divisors other than 1 and themselves. For example, 3 is a prime number because it is divisible only by 1 and 3.

• Composite numbers: Natural numbers greater than 1 that are divisible by more than two numbers. For example, 12 is a composite number because it is divisible by 1, 2, 3, 4, 6, and 12.

• 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.

• Divisibility rules: A set of rules to determine if one number is divisible by another without performing full division. For example, a number is divisible by 3 if the sum of its digits is divisible by 3.

• Sieve of Eratosthenes: A method used to find all prime numbers up to a specified integer by iteratively marking the multiples of each prime number starting from 2.