There are two main types of numbers —

Prime numbers and 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 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 1412 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 1412 has more than two factors, it is not a prime number. Several methods can be used to distinguish between prime and composite numbers: 

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

The counting divisors method involves counting the number of divisors to categorize numbers as prime or composite. Based on the count of the divisors, we categorize numbers accordingly. - If there is a total count of only 2 divisors, then the number is prime.  If the count is more than 2, then the number is composite. Let’s check whether 1412 is prime or composite.

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

Step 2: Divide 1412 by 2. It is divisible by 2, so 2 is a factor of 1412.

Step 3: Continue to check divisibility by subsequent numbers.

Step 4: You can simplify checking divisors up to the square root of 1412.

Step 5: Upon checking further, 1412 is also divisible by other numbers like 4, 353, and 706.

Since 1412 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. It is called the Divisibility Test Method. 

Divisibility by 2: The number in the ones' place value is 2, an even number, which means that 1412 is divisible by 2. 

Divisibility by 3: The sum of the digits in 1412 is 8. Since 8 is not divisible by 3, 1412 is also not divisible by 3. 

Divisibility by 5: The unit’s place digit is 2, so 1412 is not divisible by 5. 

Divisibility by 7: Using the divisibility rule for 7, 1412 is not divisible by 7. 

Divisibility by 11: The alternating sum of the digits is not a multiple of 11, so 1412 is not divisible by 11.

Since 1412 is divisible by multiple numbers, it has more than two factors, confirming it is a composite number.

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

Step 1: Write numbers in a sequence.

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 desired range. Through this process, we will have a list of prime numbers.

Since 1412 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 1412 as 2 × 706.

Step 2: In 2 × 706, 706 is a composite number. Further, break 706 into 2 × 353.

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

Hence, the prime factorization of 1412 is 2 × 2 × 353.

• Composite numbers: Natural numbers greater than 1 that are divisible by more than 2 numbers are called composite numbers. For example, 1412 is a composite number because it is divisible by 1, 2, 4, 353, 706, and 1412.

• Divisibility: A number is divisible by another number if you can divide them without leaving a remainder.

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

• Co-prime numbers: Two numbers are co-prime if their greatest common divisor (GCD) is 1.

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