Is 1167 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 1167 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 1167 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:

• 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 1167 is prime or composite.

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

Step 2: Divide 1167 by 2. It is not divisible by 2, so 2 is not a factor of 1167.

Step 3: Divide 1167 by 3. It is divisible by 3, so 3 is a factor of 1167.

Step 4: You can simplify checking divisors up to 1167 by finding the root value. We then need to only check divisors up to the root value.

Step 5: When we divide 1167 by 3, it is divisible by 3. Since 1167 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. This is called the Divisibility Test Method.

Divisibility by 2: The number in the ones' place value in 1167 is 7, which is odd. Therefore, 1167 is not divisible by 2.

Divisibility by 3: The sum of the digits in the number 1167 is 15. Since 15 is divisible by 3, 1167 is also divisible by 3.

Divisibility by 5: The unit’s place digit is 7. Therefore, 1167 is not divisible by 5. Since 1167 is divisible by 3, 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 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 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 100.

Since 1167 is not present in this list, we can determine it is a composite number using other methods.

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 1167 as 3 × 389.

Step 2: In this factorization, 3 is a prime number, but 389 needs further checking.

Step 3: Check if 389 is a prime number. It cannot be divided evenly by any number other than 1 and itself up to its square root.

Therefore, the prime factorization of 1167 is 3 × 389.

• 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 it 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. For example, the prime factorization of 18 is 2 × 3 × 3.

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

• Sieve of Eratosthenes: An ancient algorithm used to find all prime numbers up to a specified integer.

• Factors: The numbers that divide the number exactly without leaving a remainder are called factors. For example, the factors of 4 are 1, 2, and 4 because they divide 4 completely.