Is 1236 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 1236 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 1236 has more than two factors, it is not a prime number. A few methods are used to distinguish between prime and composite numbers. Some 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 1236 is prime or composite.

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

Step 2: Divide 1236 by 2. It is divisible by 2, so 2 is a factor of 1236.

Step 3: Divide 1236 by 3. It is divisible by 3, so 3 is a factor of 1236.

Step 4: You can simplify checking divisors up to the square root of 1236.

Step 5: When we divide 1236 by numbers such as 2, 3, and 4, it is divisible by 2 and 3.

Since 1236 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 6. Six is an even number, which means that 1236 is divisible by 2. 

Divisibility by 3: The sum of the digits in the number 1236 is 12. Since 12 is divisible by 3, 1236 is also divisible by 3. 

Divisibility by 5: The unit’s place digit is 6. Therefore, 1236 is not divisible by 5. 

Divisibility by 7: For 1236, double the last digit (6 × 2 = 12). Subtract it from the rest of the number (123 - 12 = 111). Since 111 is divisible by 7, 1236 is divisible by 7. 

Divisibility by 11: In 1236, the sum of the digits in odd positions is 9, and the sum of the digits in even positions is 6. The difference is 3, which is not divisible by 11, so 1236 is not divisible by 11.

Since 1236 is divisible by numbers other than 1 and itself, it has more than two factors and 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 grid.

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 the next unmarked number as a prime

Through this process, we will have a list of prime numbers. As 1236 is not on the list, 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 1236 as 2 × 618.

Step 2: In 2 × 618, 618 is a composite number. Further, break 618 into 2 × 309.

Step 3: Break 309 into 3 × 103.

Step 4: 103 is a prime number. Hence, the prime factorization of 1236 is 2 × 2 × 3 × 103.

• 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: A number is divisible by another if the remainder is zero when divided. 

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

• Co-prime numbers: Two numbers are co-prime if their greatest common divisor (GCD) is 1. 

• Sieve of Eratosthenes: A method to find all prime numbers up to a specified integer.