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 1410 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 1410 has more than two factors, it is not a prime number. A few methods are used to distinguish between prime and composite numbers: 

• 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 1410 is prime or composite.

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

Step 2: Divide 1410 by 2. It is divisible by 2, so 2 is a factor of 1410.

Step 3: Divide 1410 by 3. It is divisible by 3, so 3 is a factor of 1410.

Step 4: You can simplify checking divisors up to 1410 by finding the square root value. We then need to only check divisors up to the square root value.

Since 1410 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 or not. It is called the Divisibility Test Method. 

Divisibility by 2: The number in the ones' place value is 0, which is an even number, meaning that 1410 is divisible by 2. 

Divisibility by 3: The sum of the digits in the number 1410 is 6. Since 6 is divisible by 3, 1410 is also divisible by 3. 

Divisibility by 5: The unit’s place digit is 0. Therefore, 1410 is divisible by 5. 

Divisibility by 7: For 1410, the divisibility test by 7 requires more steps, and further factorization shows it is not prime. 

Divisibility by 11: The sum of the digits in odd positions is 2, and the sum of the digits in even positions is 5. This means that 1410 is not divisible by 11.

Since 1410 is divisible by multiple numbers, it has more than two factors. Therefore, 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 following steps.

Step 1: Write numbers starting from 1 onwards in rows and 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 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 for numbers up to 100 or beyond. 1410 is not present in any basic prime number list, so it is a composite 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 can write 1410 as 2 × 705.

Step 2: In 705, it is further divisible by 3, giving us 3 × 235.

Step 3: Continue breaking down until all factors are prime.

Finally, 1410 is 2 × 3 × 5 × 47. Hence, the prime factorization of 1410 is 2 × 3 × 5 × 47.

•  Composite numbers: Natural numbers greater than 1 that are divisible by more than 2 numbers are called composite numbers. For example, 1410 is a composite number because it is divisible by multiple numbers. 

• Divisibility Test: A method used to determine if one number is divisible by another without performing division. 

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

• Sieve of Eratosthenes: A systematic method used to find all prime numbers up to a certain limit. 

• Prime numbers: Numbers greater than 1 with no divisors other than 1 and themselves.