There are two main types of numbers —

prime numbers and composite numbers — based 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 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 that is 1.
   
• As 1408 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 1408 has more than two factors, it is not a prime number. A few methods are used to distinguish between prime and composite numbers. These methods are: 

• 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, the number is composite. Let’s check whether 1408 is prime or composite.

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

Step 2: Divide 1408 by 2. It is divisible by 2, so 2 is a factor of 1408.

Step 3: Divide 1408 by 3. It is not divisible by 3, so 3 is not a factor of 1408.

Step 4: To simplify, check divisors up to the square root value of 1408.

Step 5: When we divide 1408 by 2, 4, and 8, it is divisible by these numbers.

Since 1408 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. This is called the Divisibility Test Method. 

Divisibility by 2: The number in the ones' place is 8, an even number, indicating that 1408 is divisible by 2. 

Divisibility by 3: The sum of the digits in 1408 is 13. Since 13 is not divisible by 3, 1408 is also not divisible by 3. 

Divisibility by 5: The unit’s place digit is 8, so 1408 is not divisible by 5. 

Divisibility by 7: Double the last digit (8 × 2 = 16), subtract from the rest of the number (140 - 16 = 124). Since 124 is not divisible by 7, 1408 is not divisible by 7. 

Divisibility by 11: The difference between the sum of digits in odd and even positions is 1, which is not divisible by 11.

Since 1408 is divisible by 2 and other numbers like 4, it has more than two factors, making it a composite number.

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

Step 1: Write numbers from 1 to 100 in 10 rows and 10 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 multiples of 2.

Step 4: Mark 3 because it is a prime number and cross out all 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 have a list of prime numbers from 1 to 100.

The list is 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97. 1408 is not on the list, so it is a composite number.

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

Step 1: We can write 1408 as 2 × 704.

Step 2: In 2 × 704, 704 is a composite number. Further, break 704 into 2 × 352.

Step 3: Continue breaking down 352 into 2 × 176, then 176 into 2 × 88, and 88 into 2 × 44, and finally 44 into 2 × 22, and 22 into 2 × 11.

The prime factorization of 1408 is 2 × 2 × 2 × 2 × 2 × 2 × 2 × 11.

•  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. 

• Prime numbers: Natural numbers greater than 1 that have no divisors other than 1 and itself. For example, 7 is a prime number. 

• Divisibility test: A method or rule to determine if one number is divisible by another without performing division. 

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

• Factors: Numbers that divide a number exactly without leaving a remainder. For example, the factors of 4 are 1, 2, and 4 because they divide 4 completely.