Is 1138 a Prime Number?

There are two primary classifications of numbers —

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 instance, 3 is a prime number because it is divisible by 1 and itself.

A composite number, on the other hand, 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 have a few properties such as:

• 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 1138 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 1138 has more than two factors, it is not a prime number.
   
• Several 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 counting divisors method involves counting the number of divisors to categorize the numbers as prime or composite. 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 is prime.
   
• If the count is more than 2, then the number is composite.
   

Let’s check whether 1138 is prime or composite.
 

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

Step 2: Divide 1138 by 2. It is divisible by 2, so 2 is a factor of 1138.

Step 3: Divide 1138 by 3. It is not divisible by 3, so 3 is not a factor of 1138.

Step 4: You can simplify checking divisors up to 1138 by finding the root value. We then need to only check divisors up to the root value.

Since 1138 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 is 8. Eight is an even number, which means that 1138 is divisible by 2.

Divisibility by 3: The sum of the digits in the number 1138 is 13. Since 13 is not divisible by 3, 1138 is also not divisible by 3.

Divisibility by 5: The unit’s place digit is 8. Therefore, 1138 is not divisible by 5.

Divisibility by 7: The last digit in 1138 is 8. To check divisibility by 7, double the last digit (8 × 2 = 16). Then, subtract it from the rest of the number (113 - 16 = 97). Since 97 is not divisible by 7, 1138 is also not divisible by 7.

Divisibility by 11: In 1138, the sum of the digits in odd positions is 4, and the sum of the digits in even positions is 3. This means that 1138 is not divisible by 11. Since 1138 is divisible by 2, it has more than two factors. Therefore, it is a composite number.

The prime number chart is a tool created using a method called “The Sieve of Eratosthenes.”

In this method, we follow the following steps:

Step 1: Write numbers in rows and columns up to a certain limit.

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 with the next unmarked number.

Through this process, we can identify the list of prime numbers. Since 1138 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 multiplying those factors to obtain the original number.

Step 1: We can write 1138 as 2 × 569.

Step 2: In 2 × 569, check if 569 is a composite number.

Upon checking, 569 is a prime number itself. Therefore, the prime factorization of 1138 is 2 × 569.

• Composite numbers: Natural numbers greater than 1 that are divisible by more than 2 numbers are called composite numbers. For example, 8 is a composite number because it is divisible by 1, 2, 4, and 8.
   
• 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: Set of rules that help determine whether one number is divisible by another without performing division. For example, a number is divisible by 2 if its last digit is even.
   
• Prime numbers: Numbers greater than 1 that have no divisors other than 1 and itself. For example, 7 is a prime number.
   
• Sieve of Eratosthenes: An ancient algorithm used to find all prime numbers up to a specified integer.