Is 1242 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.

As 1242 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 1242 has more than two factors, it is not a prime number. A few methods are used to distinguish between prime and composite numbers, including:

• 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 are only 2 divisors in total, the number is prime.

- If the count is more than 2, the number is composite.

Let’s check whether 1242 is prime or composite.

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

Step 2: Divide 1242 by 2. It is divisible by 2, so 2 is a factor of 1242.

Step 3: Divide 1242 by 3. It is divisible by 3, so 3 is a factor of 1242.

Step 4: You can simplify checking divisors of 1242 by finding the root value. We then need to check divisors up to the root value.

Since 1242 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 one's place is 2, which is even, so 1242 is divisible by 2.

- Divisibility by 3: The sum of the digits in 1242 is 9 (1+2+4+2). Since 9 is divisible by 3, 1242 is also divisible by 3.

- Divisibility by 5: The unit's place digit is 2, so 1242 is not divisible by 5.

- Divisibility by 7: To check divisibility by 7, double the last digit (2 × 2 = 4). Then, subtract it from the rest of the number (124 - 4 = 120). Since 120 is divisible by 7, 1242 is also divisible by 7.

- Divisibility by 11: In 1242, the alternating sum of the digits (1 - 2 + 4 - 2) is 1, so 1242 is not divisible by 11. Since 1242 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 using a method called “The Sieve of Eratosthenes.” In this method, we follow these steps:

Step 1: Write numbers from 1 to 100 in 10 rows and 10 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 until you reach a table consisting of marked and crossed boxes, except 1. Through this process, we will have a list of prime numbers from 1 to 100. The list is 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97.

Since 1242 is not on the list and is greater than 100, we can further check using its factors to confirm it's composite.

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 1242 as 2 × 621.

Step 2: Further break down 621: 621 is 3 × 207.

Step 3: Break down 207: 207 is 3 × 69.

Step 4: Break down 69: 69 is 3 × 23.

The prime factorization of 1242 is 2 × 3 × 3 × 3 × 23.

• 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 12 is divisible by 1, 2, 3, 4, 6, and 12.
  
   
• Prime factorization: The process of expressing a number as the product of its prime factors.
  
   
• Divisibility rules: A set of rules that help determine if one number is divisible by another without performing division.
  
   
• Factors: The numbers that divide a number exactly without leaving a remainder. For example, the factors of 4 are 1, 2, and 4 because they divide 4 completely.
  
   
• Perfect square: A number that is the square of an integer. For example, 16 is a perfect square because it is 4 squared.