Is 1132 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. Since 1132 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 1132 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 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 1132 is prime or composite.

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

Step 2: Divide 1132 by 2. It is divisible by 2, so 2 is a factor of 1132.

Step 3: Divide 1132 by 3. It is not divisible by 3, so 3 is not a factor of 1132.

Step 4: You can simplify checking divisors up to 1132 by finding the root value. We then need to check divisors only up to the root value.

Step 5: When we divide 1132 by 2, 4, 11, and other numbers, it is divisible by some of them.

Since 1132 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 2, which is an even number, meaning that 1132 is divisible by 2.

Divisibility by 3: The sum of the digits in the number 1132 is 7. Since 7 is not divisible by 3, 1132 is also not divisible by 3.

Divisibility by 5: The unit’s place digit is 2. Therefore, 1132 is not divisible by 5.

Divisibility by 7: Using the divisibility rule for 7, we can determine that 1132 is not divisible by 7.

Divisibility by 11: Using the divisibility rule for 11, we find that 1132 is not divisible by 11.

Since 1132 is divisible by numbers besides 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 these steps.

Step 1: Write numbers in a range, such as 1 to 1200, in a grid of 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 within our range. 1132 is not present in the list of prime numbers, so it is a composite number.

Prime factorization is a process of breaking down a number into prime factors and then multiplying those factors to obtain the original number.

Step 1: We can write 1132 as 2 × 566.

Step 2: In 2 × 566, 566 is a composite number. Further, break down 566 into prime factors, such as 2 × 283.

Step 3: Now we get the product consisting of only prime numbers. Hence, the prime factorization of 1132 is 2 × 2 × 283.

• 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 numbers: Numbers greater than 1 with only two factors, 1 and themselves.
   
• Divisibility: A number is divisible by another if there is no remainder after division.
   
• Prime factorization: The process of breaking down a number into its prime factors.
   
• Co-prime numbers: Two numbers with no common factors other than 1.