Is 1224 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 such as:

• 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 1224 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 1224 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 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 1224 is prime or composite.

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

Step 2: Divide 1224 by 2. It is divisible by 2, so 2 is a factor of 1224.

Step 3: Divide 1224 by 3. It is divisible by 3, so 3 is a factor of 1224.

Step 4: You can simplify checking divisors up to 1224 by finding the root value. We then need to only check divisors up to the root value.

Step 5: When we divide 1224 by 2, 3, 4, 6, and 8, it is divisible by all of these.

Since 1224 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 4. Four is an even number, which means that 1224 is divisible by 2.

Divisibility by 3: The sum of the digits in the number 1224 is 9. Since 9 is divisible by 3, 1224 is also divisible by 3.

Divisibility by 5: The unit’s place digit is 4. Therefore, 1224 is not divisible by 5.

Divisibility by 7: The last digit in 1224 is 4. Double the last digit (4 × 2 = 8), then subtract it from the rest of the number (122 - 8 = 114). Since 114 is divisible by 7, 1224 is divisible by 7.

Divisibility by 11: In 1224, the sum of the digits in odd positions is 4, and the sum of the digits in even positions is 4. The difference is 0, which is divisible by 11, so 1224 is divisible by 11.

Since 1224 is divisible by more than two numbers, 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 in multiple 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 table consisting of marked and crossed boxes, except 1. Through this process, we will have a list of prime numbers.

Since 1224 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 multiplying those factors to obtain the original number.

Step 1: We can write 1224 as 2 × 612.

Step 2: In 2 × 612, 612 is a composite number. Further, break the 612 into 2 × 306.

Step 3: Continuing this process, we further break it down into 2 × 153, then 3 × 51, and finally 3 × 17.

Hence, the prime factorization of 1224 is 2 × 2 × 2 × 3 × 3 × 17.

• Composite numbers: Natural numbers greater than 1 that are divisible by more than 2 numbers are called composite numbers. For example, 1224 is a composite number because it has multiple factors.

• Prime factorization: The process of breaking down a composite number into its prime factors.

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

• Sieve of Eratosthenes: An ancient algorithm for finding all prime numbers up to a specified integer.

• Co-prime numbers: Two numbers that have no common factors other than 1.