There are two main types of numbers based on the number of factors they have—

prime numbers and composite numbers.

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: 

• 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 1076 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 1076 has more than two factors, it is not a prime number. Several methods are used to distinguish between prime and composite numbers, such as: 

• Counting Divisors Method 
   
• Divisibility Test 
   
• Prime Number Chart 
   
• Prime Factorization

The method in which we count the number of divisors to categorize 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 is prime.  If the count is more than 2, then the number is composite. Let’s check whether 1076 is prime or composite.

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

Step 2: Divide 1076 by 2. It is divisible by 2, so 2 is a factor of 1076.

Step 3: Divide 1076 by 3. It is not divisible by 3, so 3 is not a factor of 1076.

Step 4: You can simplify checking divisors up to 1076 by finding the square root. We then need to check divisors up to the root value.

Since 1076 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 last digit of 1076 is 6, which is an even number, so 1076 is divisible by 2. 

Divisibility by 3: The sum of the digits in 1076 is 1 + 0 + 7 + 6 = 14. Since 14 is not divisible by 3, 1076 is also not divisible by 3. 

Divisibility by 5: The unit’s place digit is 6, which is not 0 or 5, so 1076 is not divisible by 5. 

Divisibility by 7: Double the last digit (6 × 2 = 12) and subtract it from the rest of the number (107 - 12 = 95). Since 95 is divisible by 7, 1076 is also divisible by 7. 

Divisibility by 11: The alternating sum of the digits (1 - 0 + 7 - 6 = 2) is not divisible by 11, so 1076 is not divisible by 11.

Since 1076 is divisible by more than two numbers, 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 these steps:

Step 1: Write numbers from 1 to 100 in rows and columns.

Step 2: Leave 1 unmarked 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 as a prime number and cross out all multiples of 3.

Step 5: Continue this process until the list is complete. Through this process, we have a list of prime numbers from 1 to 100.

Since 1076 is not in this list, it confirms it is not prime.

Prime factorization is a process of breaking down a number into its prime factors, then multiplying those factors to obtain the original number.

Step 1: We can write 1076 as 2 × 538.

Step 2: Break 538 further into 2 × 269.

Step 3: Now, 269 is a prime number.

Thus, the prime factorization of 1076 is 2 × 2 × 269.

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

• Prime numbers: Numbers greater than 1 that have no divisors other than 1 and themselves.

• Divisibility rules: Guidelines used to determine whether a number is divisible by another without performing full division.

• Prime factorization: The expression of a number as the product of its prime factors.

• Factors: Numbers that divide another number exactly without leaving a remainder.