Is 1239 a Prime Number?

There are two primary types of numbers — prime numbers and composite numbers, based on the number of factors they have. 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 have certain properties, such as: -

• 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 1239 has more than two factors, it is not a prime number.

The defining characteristic of a prime number is that it has only two divisors: 1 and itself. Since 1239 has more than two factors, it is not a prime number. Several methods can be used to distinguish between prime and composite numbers, including: -

1. Counting Divisors Method 
2. Divisibility Test 
3. Prime Number Chart 
4. Prime Factorization

The counting divisors method involves counting the number of divisors to categorize numbers as prime or composite. Based on the count of the divisors, numbers are categorized as follows: 

• If there is a total count of only 2 divisors, then the number is prime. 
• If the count is more than 2, then the number is composite.

Let’s check whether 1239 is prime or composite.

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

Step 2: Divide 1239 by 2. It is not divisible by 2, so 2 is not a factor of 1239.

Step 3: Divide 1239 by 3. It is divisible by 3, so 3 is a factor of 1239.

Step 4: You can simplify checking divisors up to 1239 by finding the square root value, then only check divisors up to this root value.

Since 1239 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. This is called the Divisibility Test Method. -

Divisibility by 2: The number in the ones' place is 9, which is odd, meaning that 1239 is not divisible by 2. -

Divisibility by 3: The sum of the digits in 1239 is 1 + 2 + 3 + 9 = 15. Since 15 is divisible by 3, 1239 is also divisible by 3. -

Divisibility by 5: The unit’s place digit is 9. Therefore, 1239 is not divisible by 5. -

Divisibility by 7: The last digit in 1239 is 9. Double the last digit (9 × 2 = 18). Subtract it from the rest of the number (123 - 18 = 105). Since 105 is divisible by 7, 1239 is also divisible by 7. -

Divisibility by 11: In 1239, the sum of the digits in odd positions is 1 + 3 = 4, and the sum of the digits in even positions is 2 + 9 = 11. Since 4 - 11 = -7 is not divisible by 11, 1239 is not divisible by 11.

Since 1239 is divisible by more than two numbers, it is a composite number.

The prime number chart is a tool created using a method called “The Sieve of Eratosthenes.” In this method, the following steps are followed:

Step 1: Write numbers from 1 to 1000 in a systematic order.

Step 2: Leave 1 without marking, as it is neither prime nor composite.

Step 3: Mark 2 because it is a prime number and cross out all multiples of 2.

Step 4: Mark 3 because it is a prime number and cross out all 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.

1239 is not 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 and then multiplying those factors to obtain the original number.

Step 1: We can write 1239 as 3 × 413.

Step 2: In 413, check further divisibility. 413 can be factored as 7 × 59.

Step 3: Now we get the prime factorization of 1239 as 3 × 7 × 59.

• Composite Numbers: Natural numbers greater than 1 that have more than two factors. For example, 8 is a composite number because it is divisible by 1, 2, 4, and 8.

• Factors: Numbers that divide another number exactly without leaving a remainder. For example, the factors of 10 are 1, 2, 5, and 10. 

• Divisibility Test: A set of rules to determine whether one number is divisible by another. For instance, a number is divisible by 3 if the sum of its digits is divisible by 3. 

• Prime Factorization: The process of expressing a number as the product of its prime factors. For example, the prime factorization of 28 is 2 × 2 × 7. 

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