Is 1130 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 that is 1.

As 1130 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 1130 has more than two factors, it is not a prime number.
   
• A 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 numbers as prime or composite.

• 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 1130 is prime or composite.

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

Step 2: Divide 1130 by 2. It is divisible by 2, so 2 is a factor of 1130.

Step 3: Continue dividing by subsequent integers to check for additional factors.

Since 1130 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 0, which means that 1130 is divisible by 2.

Divisibility by 3: The sum of the digits in the number 1130 is 5. Since 5 is not divisible by 3, 1130 is not divisible by 3.

Divisibility by 5: The unit’s place digit is 0. Therefore, 1130 is divisible by 5.

Divisibility by 7, 11, and others: Continue checking using divisibility rules.

Since 1130 is divisible by numbers other than 1 and itself, 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 large table.

Step 2: Leave 1 without coloring or crossing, as it is neither prime nor composite.

Step 3: Mark prime numbers and cross out all their multiples.

Through this process, we will have a list of prime numbers.

Since 1130 is not 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 1130 as 2 × 565.
 

Step 2: In 2 × 565, further break down 565 into prime factors, such as 5 × 113.
 

Step 3: The prime factorization of 1130 is 2 × 5 × 113.
 

• 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: Set of rules to determine if a number is divisible by another number without performing full division.
   
• Prime factorization: The process of expressing a number as the product of its prime factors.
   
• Sieve of Eratosthenes: An ancient algorithm used to find all prime numbers up to a specified integer.
   
• Co-prime numbers: Two numbers that have no common factors other than 1.