Is 1039 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 1039 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 1039 has only two factors, it is a prime number. A few 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 1039 is prime or composite.

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

Step 2: Divide 1039 by numbers starting from 2 up to the square root of 1039, which is approximately 32.

Step 3: 1039 is not divisible by any number other than 1 and itself.

Since 1039 has only 2 divisors, 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.

1039 is not divisible by 2 because it is not an even number.

1039 is not divisible by 3 because the sum of its digits (1 + 0 + 3 + 9 = 13) is not divisible by 3.

1039 is not divisible by 5 because it does not end in 0 or 5. 1039 is not divisible by 7. The divisibility rule for 7 involves multiplying the last digit by 2 and subtracting from the rest, which does not yield a multiple of 7.

1039 is not divisible by 11, as the difference between the sum of its alternating digits is not a multiple of 11.

Since 1039 is not divisible by any number other than 1 and itself, 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 1000 in rows and 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 can identify prime numbers.

Since 1039 is not divisible by any number other than 1 and itself, 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 1039 is only divisible by 1 and 1039, there are no other prime factors.

Hence, 1039 itself is a prime number.

• Prime numbers: Natural numbers greater than 1 that have no divisors other than 1 and themselves.
   
• Composite numbers: Natural numbers greater than 1 that are divisible by more than 2 numbers.


• Divisibility rules: Set of rules that help determine if a number is divisible by another without performing division.
   
• Sieve of Eratosthenes: An ancient algorithm used to find all primes up to any given limit.
   
• Prime factorization: Process of breaking down a number into its prime factors.