Is 3211 a Prime Number?

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.

3211 has only two factors, 1 and 3211, which makes it a prime number.

The characteristic of a prime number is that it has only two divisors: 1 and itself. Since 3211 has exactly two factors, it is a prime number. A few methods to verify if a number is prime include:

• 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 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 3211 is prime or composite.

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

Step 2: Check divisibility by smaller prime numbers such as 2, 3, 5, 7, 11, etc., up to the square root of 3211 (approximately 56.63). 3211 is not divisible by any of these numbers.

Since 3211 has exactly 2 divisors, 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: 3211 is odd, so it is not divisible by 2.

- Divisibility by 3: The sum of the digits in 3211 is 7, which is not divisible by 3.

- Divisibility by 5: The unit’s place digit is 1, so it is not divisible by 5.

- Divisibility by 7, 11, etc.: 3211 is not divisible by these numbers either.

Since 3211 is not divisible by any prime numbers up to its square root, it has only two factors, 1 and 3211, confirming it as 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 these steps:

Step 1: Write numbers in a sequence, for example, from 1 to 100, or extend it as needed.

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 with subsequent prime numbers.

Although 3211 is not within a small range like 1 to 100, further extending the process would reveal 3211 as a prime number since it would not be crossed out.

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

Step 1: Start dividing 3211 by the smallest prime numbers (2, 3, 5, 7, 11, etc.) up to its square root.

Step 2: Since 3211 is not divisible by any of these, it cannot be factored further using smaller primes.

3211 can only be expressed as 1 × 3211, confirming that it is a prime number.

• Prime numbers: Natural numbers greater than 1 with only two divisors: 1 and itself.
  
   
• Composite numbers: Natural numbers greater than 1 that are divisible by more than 2 numbers.
  
   
• Divisibility test: A method to determine if one number can be divided by another without leaving a remainder.
  
   
• Factors: The numbers that divide a given number exactly without leaving a remainder.
  
   
• Prime factorization: The process of expressing a number as a product of its prime factors.