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 1075 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 1075 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 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 1075 is prime or composite. 

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

Step 2: Divide 1075 by 2. It is not divisible by 2, so 2 is not a factor of 1075. 

Step 3: Divide 1075 by 3. It is not divisible by 3, so 3 is not a factor of 1075. 

Step 4: Continue this process for divisors up to the square root of 1075. 

Step 5: When we divide 1075 by 5, it is divisible, so 5 is a factor.

Since 1075 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: 1075 is an odd number, so it is not divisible by 2. 

Divisibility by 3: The sum of the digits in the number 1075 is 13. Since 13 is not divisible by 3, 1075 is not divisible by 3. 

Divisibility by 5: The unit’s place digit is 5, so 1075 is divisible by 5. 

Divisibility by 7: Subtract twice the last digit from the rest of the number (107 - 10 = 97). Since 97 is not divisible by 7, 1075 is not divisible by 7. 

Divisibility by 11: Alternating sum of digits is 1 - 0 + 7 - 5 = 3. Since 3 is not divisible by 11, 1075 is not divisible by 11.

Since 1075 is divisible by 5, it has more than two factors. Therefore, it is a composite number.

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

Step 1: Write numbers in a range, such as 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 largest number in the range. Through this process, we will have a list of prime numbers within the range.

Since 1075 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 and then multiplying those factors to obtain the original number.

Step 1: We can write 1075 as 5 × 215. 

Step 2: In 5 × 215, 215 is a composite number. Further, break 215 into 5 × 43. 

Step 3: Now, we get the product consisting of only prime numbers.

Hence, the prime factorization of 1075 is 5 × 5 × 43.

•  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 two numbers. 

• Divisibility rules: Guidelines to determine if one number is divisible by another without performing division. 

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

• Co-prime numbers: Two numbers with no common factors other than 1.