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 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 1399 has only two factors, it is a prime number.

The characteristic of a prime number is that it has only two divisors: 1 and itself. Since 1399 has exactly two factors, it is a prime number. Few methods are used to distinguish between prime and composite numbers. A few methods are:

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

The method in which we count the number of divisors to categorize the 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 1399 is prime or composite.

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

Step 2: Divide 1399 by 2. It is not divisible by 2, so 2 is not a factor of 1399.

Step 3: Divide 1399 by 3. It is not divisible by 3, so 3 is not a factor of 1399.

Step 4: You can simplify checking divisors up to 1399 by finding the root value. We then need to only check divisors up to the root value, which is approximately 37.4.

Step 5: When we divide 1399 by prime numbers such as 5, 7, 11, 13, 17, 19, 23, 29, 31, and 37, it is not divisible by any of these.

Since 1399 has only 2 divisors, 1 and 1399, it is a prime 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 number in the ones' place value is 9. Nine is an odd number, which means that 1399 is not divisible by 2.

Divisibility by 3: The sum of the digits in the number 1399 is 22. Since 22 is not divisible by 3, 1399 is also not divisible by 3.

Divisibility by 5: The unit’s place digit is 9. Therefore, 1399 is not divisible by 5.

Divisibility by 7: Subtract twice the last digit from the rest of the number (139 - 18 = 121). Since 121 is not divisible by 7, 1399 is also not divisible by 7.

Divisibility by 11: In 1399, the difference between the sum of the digits in odd positions (1 + 9 = 10) and the sum of the digits in even positions (3 + 9 = 12) is 2. This would mean that 1399 is not divisible by 11.

Since 1399 is not divisible by any of these common divisors, it is a prime number.

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

Step 1: Write numbers in sequence 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 because it is a prime number and cross out all the 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 will have a list of prime numbers. If the number in question is not crossed out, it is prime.

Since 1399 is not divisible by any prime numbers up to its square root, it is a prime number.

Prime factorization is a process of breaking down a number into prime factors. Then multiply those factors to obtain the original number.

Step 1: We attempt to write 1399 as a product of smaller numbers.

Step 2: Since 1399 is not divisible by any prime numbers less than its square root, 1399 is itself a prime factor.

Step 3: Therefore, the prime factorization of 1399 is 1399 itself.

• Prime numbers: Natural numbers greater than 1 that have no divisors other than 1 and themselves. For example, 5 is a prime number.

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

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

• Divisibility: A concept in mathematics where one number can be divided by another without leaving a remainder.

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