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 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.
   
• To determine if 1411 is a prime number, we need to check its factors.

The characteristic of a prime number is that it has only two divisors: 1 and itself. Since 1411 has more than two factors, it is not 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 1411 is prime or composite.

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

Step 2: Divide 1411 by 2. It is not divisible by 2, so 2 is not a factor of 1411.

Step 3: Divide 1411 by 3. It is not divisible by 3, so 3 is not a factor of 1411.

Step 4: You can simplify checking divisors up to 1411 by finding the root value. We then need to only check divisors up to the root value, which is approximately 37.

Step 5: When we divide 1411, it is divisible by 29. Since 1411 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 1, which is odd, so 1411 is not divisible by 2.

Divisibility by 3: The sum of the digits in the number 1411 is 7. Since 7 is not divisible by 3, 1411 is also not divisible by 3.

Divisibility by 5: The unit’s place digit is 1. Therefore, 1411 is not divisible by 5.

Divisibility by 7: Using divisibility rules, 1411 is not divisible by 7.

Divisibility by 29: 1411 is divisible by 29. Since 1411 is divisible by 29, 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 in a range, for example, 1 to 1500.

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.

1411 is not present in the list of prime numbers, 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 1411 as 29 × 48.65.

Step 2: Since 48.65 is not an integer, check further factorizations.

Step 3: 1411 is divisible by 29, confirming it is not a prime.

Hence, the prime factorization of 1411 involves 29.

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

• Divisibility rules: Guidelines that help 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.

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

• Co-prime numbers: Two numbers with no common factors other than 1.