Is 1227 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 1227 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 1227 has more than two factors, it is not a prime number. Several 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 1227 is prime or composite.

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

Step 2: Divide 1227 by 2. It is not divisible by 2, as it is an odd number.

Step 3: Divide 1227 by 3. The sum of the digits (1 + 2 + 2 + 7 = 12) is divisible by 3, so 1227 is divisible by 3.

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

Since 1227 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 7, which is odd. Therefore, 1227 is not divisible by 2. 

Divisibility by 3: The sum of the digits in the number 1227 is 12. Since 12 is divisible by 3, 1227 is divisible by 3. 

Divisibility by 5: The unit’s place digit is 7. Therefore, 1227 is not divisible by 5. 

Divisibility by 7: To check divisibility by 7, double the last digit (7 × 2 = 14). Then, subtract it from the rest of the number (122 - 14 = 108). Since 108 is divisible by 7, 1227 is divisible by 7. 

Divisibility by 11: In 1227, the sum of the digits in odd positions is 1 + 2 = 3, and the sum of the digits in even positions is 2 + 7 = 9. Their difference is 6, which is not divisible by 11. Hence, 1227 is not divisible by 11.

Since 1227 is divisible by 3 and 7, it has more than two factors. Therefore, it 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 from 1 to 1000.

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 finish marking all prime numbers. Through this process, we will have a list of prime numbers from 1 to 1000.

Since 1227 is not present in the list of prime numbers, 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 1227 as 3 × 409.

Step 2: Since 409 is not divisible by 2, 3, or 5, continue with the next primes.

Step 3: 409 can be divided by 7, resulting in 409 = 7 × 58.

Step 4: 58 is further divisible by 2 and 29, resulting in 58 = 2 × 29.

Thus, the prime factorization of 1227 is 3 × 7 × 2 × 29.

• 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.

• Divisibility rules: Guidelines that help determine if one number is divisible by another without performing full division.

• Prime factorization: Breaking down a number into a product of its prime factors.

• Factors: Numbers that divide the number exactly without leaving a remainder are called factors. For example, the factors of 4 are 1, 2, and 4 because they divide 4 completely.

• Co-prime numbers: Two numbers that have only 1 as their common factor. For example, 8 and 15 are co-prime.