Numbers can generally be categorized as prime numbers or composite numbers, depending on the number of factors they have.

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 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 because they have only one common factor, which is 1.
   
• As 1341 has more than two factors, it is not a prime number.

The defining characteristic of a prime number is that it has only two divisors: 1 and itself. Since 1341 has more than two factors, it is not a prime number. Several methods can be used to distinguish between prime and composite numbers. These methods include:

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

The counting divisors method involves tallying the number of divisors to categorize numbers as either prime or composite. Based on the count, we categorize them:  If there are only 2 divisors, the number is prime. - If there are more than 2, the number is composite. Let’s check whether 1341 is prime or composite.

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

Step 2: Divide 1341 by 2. It is not divisible by 2 since it is odd.

Step 3: Divide 1341 by 3. The sum of the digits is 9, which is divisible by 3, so 1341 is divisible by 3.

Step 4: Continue checking divisors up to the approximate square root of 1341.

Step 5: 1341 is divisible by 3 and 447, among others.

Since 1341 has more than 2 divisors, it is a composite number.

The divisibility test involves using a set of rules to check whether a number can be divided completely by another number. 

Divisibility by 2: 1341 is not divisible by 2 since it is odd.

Divisibility by 3: The sum of the digits of 1341 is 9, which is divisible by 3, so 1341 is divisible by 3. 

Divisibility by 5: The unit’s place is not 0 or 5, so 1341 is not divisible by 5. 

Divisibility by 7: Using specific divisibility rules, 1341 is not divisible by 7. 

Divisibility by 11: Using specific divisibility rules, 1341 is not divisible by 11.

Since 1341 is divisible by 3, it has more than two factors and is therefore a composite number.

The prime number chart is a tool created using a method known as “The Sieve of Eratosthenes.” In this method, we follow these steps: '

Step 1: Write numbers from 1 to 1000 in rows and columns.

Step 2: Leave 1 without marking, as it is neither prime nor composite.

Step 3: Mark 2, as it is a prime number, and cross out all multiples of 2.

Step 4: Mark 3 and cross out all multiples of 3.

Step 5: Repeat this process up to the square root of the maximum number.

1341 will not appear in the list of prime numbers, confirming it is a composite number.

Prime factorization involves breaking down a number into its prime factors and multiplying them to obtain the original number.

Step 1: We can write 1341 as 3 × 447.

Step 2: Further break down 447 into 3 × 149.

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

Hence, the prime factorization of 1341 is 3 × 3 × 149.

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

• Factors: Numbers that divide a number exactly without leaving a remainder. For example, the factors of 6 are 1, 2, 3, and 6.

• Prime factorization: The process of breaking down a number into its prime factors.

• Square Root: The number that, when multiplied by itself, gives the original number.

• Divisibility Rule: A shortcut to determine if a number is divisible by another without performing divisions.