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 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.
   
• Since 1073 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 1073 has more than two factors, it is not a prime number. 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 1073 is prime or composite.

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

Step 2: Divide 1073 by 2. It is not divisible by 2, so 2 is not a factor of 1073.

Step 3: Divide 1073 by 3. The sum of the digits is 11, which is not divisible by 3, so 1073 is not divisible by 3.

Step 4: You can simplify checking divisors up to 1073 by finding the root value, approximately 32.7, so check divisors up to 32.

Step 5: Continue checking divisibility with other prime numbers like 5, 7, 11, 13, 17, 19, and so on.

Since 1073 is divisible by 29 and 37, it has more than 2 divisors and 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: 1073 is not even, so it is not divisible by 2. 

Divisibility by 3: The sum of the digits (1+0+7+3) is 11, which is not divisible by 3. 

Divisibility by 5: The last digit is not 0 or 5, so it is not divisible by 5. 

Divisibility by 7: Applying divisibility rules for 7 reveals that 1073 is not divisible by 7. 

Continue checking with other primes like 11, 13, 17, 19, 23, 29, etc.

Since 1073 is divisible by 29 and 37, it has more than two factors and 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 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 will have a list of prime numbers.

Since 1073 is not present in the list of prime numbers, 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 start with smaller primes to test divisibility.

Step 2: 1073 is divisible by 29, resulting in 37.

Step 3: 29 and 37 are both prime numbers.

Therefore, the prime factorization of 1073 is 29 × 37.

•  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 rules: Guidelines to check if a number is divisible by another number without performing the actual division. 

• Prime factorization: The process of expressing a number as a product of its prime factors.

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

• Co-prime numbers: Two numbers are co-prime if their greatest common divisor is 1.