Is 1128 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 1128 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 1128 has more than two factors, it is not a prime number.

Few methods are used to distinguish between prime and composite numbers.

A few methods are:

• Counting Divisors Method
   
• Divisibility Test
   
• Prime Number Chart
   
• 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 1128 is prime or composite.

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

Step 2: Divide 1128 by 2. It is divisible by 2, so 2 is a factor of 1128.

Step 3: Divide 1128 by 3. The sum of its digits (1+1+2+8=12) is divisible by 3, so 3 is a factor of 1128.

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

Step 5: When we divide 1128 by 2, 3, 4, 6, 9, etc., it is divisible by several numbers. Since 1128 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. Since 8 is an even number, 1128 is divisible by 2. 

Divisibility by 3: The sum of the digits in the number 1128 is 12. Since 12 is divisible by 3, 1128 is also divisible by 3.

Divisibility by 5: The unit’s place digit is 8, so 1128 is not divisible by 5.

Divisibility by 7: Use the rule for dividing by 7. 1128÷7=161.142857... indicating it is not divisible by 7.

Divisibility by 11: Calculate the alternating sum: (1-1+2-8=-6), which is not divisible by 11.

Since 1128 is divisible by factors other than 1 and itself, 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 in a grid format, for example, 1 to 1000 in rows and columns.

Step 2: Leave 1 without marking, 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 the grid shows all prime numbers.

Through this process, we will have a list of prime numbers. 1128 is not present in the list, so 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 1128 as 2×564.

Step 2: In 2×564, 564 is a composite number. Further, break 564 into 2×282.

Step 3: Continue breaking down until you are left with only prime numbers: 2×2×3×3×47.

Step 4: The prime factorization of 1128 is 2×2×3×3×47.

• 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 factorization: The process of expressing a number as the product of its prime factors.
   
• Divisibility rules: Set of rules that help determine if one number can be divided by another without a remainder.
   
• Co-prime numbers: Two numbers that have only one common factor, which is 1.
   
• Sieve of Eratosthenes: An ancient algorithm used to find all prime numbers up to any given limit.