Is 1037 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, 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 1037 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 1037 has more than two factors, it is not a prime number. A few methods are used to distinguish between prime and composite numbers:

• 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 1037 is prime or composite.

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

Step 2: Divide 1037 by 2. It is not divisible by 2.

Step 3: Divide 1037 by 3. It is not divisible by 3.

Step 4: You can simplify checking divisors up to 1037 by finding the square root value. We then need to only check divisors up to the square root value.

Step 5: Continue checking divisibility by subsequent prime numbers like 5, 7, 11, and so on.

Since 1037 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 7, which is odd. Therefore, 1037 is not divisible by 2.

Divisibility by 3: The sum of the digits in the number 1037 is 11, which is not divisible by 3.

Divisibility by 5: The unit’s place digit is not 0 or 5. Therefore, 1037 is not divisible by 5.

Divisibility by 7, 11, etc., can be checked using respective divisibility rules.

Since 1037 is not divisible by any of these primes up to its square root, 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 numbers in a range, for instance, 1 to 1000.

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 a table consisting of marked and crossed boxes, except 1. Through this process, we will have a list of prime numbers.

1037 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: Start dividing 1037 by the smallest prime number and continue dividing the result by prime numbers until it's no longer divisible.

Step 2: For instance, if 1037 is divisible by a prime number, continue the factorization.

Step 3: The prime factorization of 1037 will show the prime numbers that multiply to give 1037.

• 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.
   
• Divisibility: A number is divisible by another if it can be divided without leaving a remainder.
   
• Prime factorization: The process of finding which prime numbers multiply together to make the original number.
   
• Co-prime numbers: Two numbers are co-prime if their greatest common divisor is 1.
   
• Natural numbers: Positive integers starting from 1, used for counting and ordering.