Is 1216 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 1216 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 1216 has more than two factors, it is not a prime number. A few methods are used to distinguish between prime and composite numbers. These methods include: -

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 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 1216 is prime or composite.

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

Step 2: Divide 1216 by 2. It is divisible by 2, so 2 is a factor of 1216.

Step 3: Divide 1216 by 3. It is not divisible by 3, so 3 is not a factor of 1216.

Step 4: You can simplify checking divisors up to 1216 by finding the square root value. We then need to only check divisors up to the square root value.

Since 1216 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. This 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 1216 is divisible by 2.

Divisibility by 3: The sum of the digits in the number 1216 is 10. Since 10 is not divisible by 3, 1216 is also not divisible by 3. 

Divisibility by 5: The unit’s place digit is 6. Therefore, 1216 is not divisible by 5. -

Divisibility by 7: The last digit in 1216 is 6. To check divisibility by 7, double the last digit (6 × 2 = 12). Then, subtract it from the rest of the number (121 - 12 = 109). Since 109 is not divisible by 7, 1216 is also not divisible by 7. -

Divisibility by 11: In 1216, the sum of the digits in odd positions is 2 + 6 = 8, and the sum of the digits in even positions is 1 + 1 = 2. Since the difference (8 - 2 = 6) is not divisible by 11, 1216 is not divisible by 11.

Since 1216 is divisible by 2 and other 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 the following steps.

Step 1: Write numbers in a range, such as 1 to 1000, in rows and 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 the end of the list. Through this process, we will have a list of prime numbers.

1216 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 and then multiplying those factors to obtain the original number.

Step 1: We can write 1216 as 2 × 608.

Step 2: In 2 × 608, 608 is a composite number. Further, break the 608 into 2 × 304.

Step 3: Continuing this process, we get 2 × 2 × 152, then 2 × 2 × 2 × 76, and finally 2 × 2 × 2 × 2 × 38, and end with 2 × 2 × 2 × 2 × 2 × 19. Now we get the product consisting of only prime numbers.

Hence, the prime factorization of 1216 is 2 × 2 × 2 × 2 × 2 × 19.

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

• Divisibility rules: A set of rules that help determine if a number is divisible by another number without performing full division.

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

• Perfect square: A number that is the square of an integer, such as 4, 9, 16, etc.