Is 1228 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 1228 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 1228 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 the numbers as prime or composite is called the counting divisors method. Based on the count of the divisors, we categorize numbers as prime or composite. -

• If there is a total count of only 2 divisors, then the number is prime. 
• If the count is more than 2, then the number is composite.

Let’s check whether 1228 is prime or composite.

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

Step 2: Divide 1228 by 2. It is divisible by 2, so 2 is a factor of 1228.

Step 3: Divide 1228 by 3. It is not divisible by 3, so 3 is not a factor of 1228.

Step 4: To simplify checking divisors, find the square root of 1228 and check divisors up to the root value.

Since 1228 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 8, an even number, which means 1228 is divisible by 2. -

Divisibility by 3: The sum of the digits in 1228 is 13. Since 13 is not divisible by 3, 1228 is not divisible by 3. -

Divisibility by 5: The unit’s place digit is 8. Therefore, 1228 is not divisible by 5. -

Divisibility by 7: Use the rule for 7 to check divisibility. Divide 1228 by 7, and it is not divisible by 7. -

Divisibility by 11: Apply the divisibility rule for 11 to see if 1228 is divisible.

Since 1228 is divisible by factors other than 1 and itself, it has more than two factors, making it a composite number.

The prime number chart is a tool created using a method called “The Sieve of Eratosthenes.” In this method, follow the steps below:

Step 1: Write numbers from 1 to 100 in 10 rows and 10 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 up to the highest square root value needed. Through this process, you will have a list of prime numbers.

Since 1228 is not on the list of prime numbers, it is a composite number.

Prime factorization is the process of breaking down a number into its prime factors. Then multiply those factors to obtain the original number.

Step 1: Begin with 1228. It can be divided by 2 to get 614.

Step 2: Divide 614 by 2 to get 307.

Step 3: 307 is a prime number, and thus, the prime factorization of 1228 is 2 × 2 × 307.

• Composite numbers: Natural numbers greater than 1 that are divisible by more than 2 numbers are called composite numbers. For example, 18 is a composite number because it is divisible by 1, 2, 3, 6, 9, and 18.

• Prime numbers: Numbers greater than 1 that are divisible only by 1 and themselves. For example, 7 is a prime number because its only divisors are 1 and 7.

• Factors: The numbers that divide a number exactly without leaving a remainder are called factors. For example, the factors of 6 are 1, 2, 3, and 6.

• Divisibility rules: A set of rules that help determine whether one number is divisible by another without performing division.

• Prime factorization: The process of breaking down a composite number into its prime factors. For example, the prime factorization of 18 is 2 × 3 × 3.