Is 1217 a Prime Number?

There are two main types of numbers based on the number of factors: prime numbers and composite numbers. 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 instance, 6 is divisible by 1, 2, 3, and 6, making it a composite number. Prime numbers follow a few properties: -

• 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 1217 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 1217 has more than two factors, it is not a prime number. A few methods are used to distinguish between prime and composite numbers: -

1. Counting Divisors Method 
2. Divisibility Test 
3. Prime Number Chart 
4. Prime Factorization

The counting divisors method involves counting the number of divisors to categorize numbers as prime or composite. 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 1217 is prime or composite.

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

Step 2: Divide 1217 by 2. It is not divisible by 2, so 2 is not a factor of 1217.

Step 3: Divide 1217 by 3. It is not divisible by 3, so 3 is not a factor of 1217.

Step 4: You can simplify checking divisors up to 1217 by finding the root value. We then need to only check divisors up to the root value.

Step 5: Continue checking divisors like 5, 7, etc., up to the square root of 1217.

Since 1217 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 7, which is odd, so 1217 is not divisible by 2. -

Divisibility by 3: The sum of the digits in the number 1217 is 11. Since 11 is not divisible by 3, 1217 is also not divisible by 3. -

Divisibility by 5: The unit’s place digit is 7. Therefore, 1217 is not divisible by 5. -

Divisibility by 7: Apply divisibility rules for 7 to check. 1217 is not divisible by 7. -

Divisibility by 11: Use the alternating sum rule for divisibility by 11. 1217 is not divisible by 11.

Since 1217 is not divisible by any of these simple tests and has more than two factors, 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 in an ordered list.

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 multiples of 2.

Step 4: Mark 3 because it is a prime number and cross out all multiples of 3.

Step 5: Repeat this process until you reach the upper bound of the chart.

Through this process, we will have a list of prime numbers. 1217 is not in this list, 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. As 1217 is a composite number, we can factor it further to find its prime factors. For example, let's say 1217 can be expressed as:

Step 1: Start with the smallest prime number and check divisibility.

Step 2: Continue with the next smallest prime and so on.

Step 3: Once you find the prime factors, you can express 1217 as a product of these prime factors.

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

• Composite numbers: Natural numbers greater than 1 that have more than two distinct divisors.

• Divisibility rules: Guidelines to quickly determine whether one number is divisible by another.

• Factors: Numbers that divide evenly into a given number, leaving no remainder.

• Perfect square: A number that is the square of an integer.