Is 1231 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 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.
• Since 1231 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 1231 has exactly two factors, it is a prime number. Few methods are used to distinguish between prime and composite numbers. A few methods are: -

1. Counting Divisors Method 
2. Divisibility Test 
3. Prime Number Chart 
4. 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 1231 is prime or composite.

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

Step 2: Check divisibility of 1231 by other numbers. Since 1231 is not divisible by any number other than 1 and 1231 itself, it has exactly two factors.

Since 1231 has only 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. 

• 1231 is not divisible by 2, as it is an odd number. 
• The sum of the digits in 1231 is 7. Since 7 is not divisible by 3, 1231 is also not divisible by 3. -
• The last digit is not 0 or 5, so 1231 is not divisible by 5. 
• For divisibility by 7, double the last digit and subtract it from the rest of the number. 123 - 2 = 121. Since 121 is not divisible by 7, 1231 is not divisible by 7. 
• 1231 is not divisible by 11, as the difference between the sum of the digits in odd positions and even positions is not a multiple of 11.

Since 1231 is not divisible by any number other than 1 and itself, 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 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 for the numbers up to 100 or more. Through this process, we can identify prime numbers.

Since 1231 is not divisible by any prime number 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. Since 1231 is not divisible by any prime number less than or equal to its square root (approximately 35), it is a prime number.

• Prime numbers: Natural numbers greater than 1 that are divisible only by 1 and themselves. 

• Composite numbers: Natural numbers greater than 1 that are divisible by more than 2 numbers. 

• Factors: The numbers that divide the number exactly without leaving a remainder. 

• Divisibility Rules: Guidelines that help determine whether a number is divisible by another number without performing full division. 

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