Is 1147 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 1147 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 1147 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 1147 is prime or composite.

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

Step 2: Divide 1147 by 2. It is not divisible by 2, so 2 is not a factor of 1147.

Step 3: Divide 1147 by 3. It is not divisible by 3, so 3 is not a factor of 1147.

Step 4: You can simplify checking divisors up to 1147 by finding the square root value, which is approximately 33.8, and check divisors up to 33.

Step 5: When we divide 1147 by 31, it is divisible, making 31 a factor of 1147. Since 1147 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 7. Since 7 is not an even number, 1147 is not divisible by 2.

Divisibility by 3: The sum of the digits in the number 1147 is 13. Since 13 is not divisible by 3, 1147 is also not divisible by 3.

Divisibility by 5: The unit’s place digit is 7. Therefore, 1147 is not divisible by 5.

Divisibility by 7: To check divisibility by 7, double the last digit (7 × 2 = 14) and subtract it from the rest of the number (114 - 14 = 100). Since 100 is not divisible by 7, 1147 is also not divisible by 7.

Divisibility by 11: In 1147, the sum of the digits in odd positions is 5, and the sum of the digits in even positions is 5. The difference is 0, which is divisible by 11, so 1147 is divisible by 11.

Since 1147 is divisible by 11, 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 from 1 to 1000 in several 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 from 1 to 1000. The list does not include 1147, 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 1147 as 31 × 37.

Step 2: Both 31 and 37 are prime numbers.

Step 3: Now we have the product consisting of only prime numbers. Hence, the prime factorization of 1147 is 31 × 37.

• 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.
   
• Sieve of Eratosthenes: An ancient algorithm used to find all prime numbers up to a specified integer.
   
• Prime factorization: The process of determining which prime numbers multiply together to form the original number.
   
• Divisibility rules: A set of rules that helps determine whether one number is divisible by another.
   
• Co-prime numbers: Two numbers that have only 1 as their common factor.