There are two main types of numbers —

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 1063 has exactly two factors, it is a prime number.

The characteristic of a prime number is that it has only two divisors: 1 and itself. Since 1063 has exactly two factors, it is a prime number. Several methods can confirm whether a number is prime or composite. These methods include:

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

The method of counting 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 numbers as prime or composite. 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 1063 is prime or composite.

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

Step 2: Check divisibility of 1063 by numbers up to its square root (approximately 32.6).

Step 3: 1063 is not divisible by any numbers other than 1 and 1063 itself.

Since 1063 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. This is called the Divisibility Test Method.

Divisibility by 2: 1063 is an odd number, so it is not divisible by 2.

Divisibility by 3: The sum of the digits (1 + 0 + 6 + 3 = 10) is not divisible by 3.

Divisibility by 5: The unit’s place digit is 3, so it is not divisible by 5.

Divisibility by 7, 11, etc.: Testing these shows no divisibility.

Since 1063 is not divisible by any number other than 1 and itself, it is a prime 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 grid format up to a certain limit.

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, 5, 7, and so on, crossing out their multiples.

Step 5: Continue this process to identify primes. 1063 is not present in the list of crossed numbers, indicating it is a prime number.

Prime factorization is a process of breaking down a number into prime factors, then multiplying those factors to obtain the original number. Since 1063 is a prime number, it cannot be factored further, and its prime factorization is simply 1063.

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

• Composite numbers: Natural numbers greater than 1 that have more than two divisors.

• Divisibility: A number's ability to be divided by another number without leaving a remainder.

• Factorization: The process of breaking down a number into a product of other numbers, specifically primes in the context of prime factorization.

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