Is 1108 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 1108 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 1108 has more than two factors, it is not a prime number. A few methods are used to distinguish between prime and composite numbers, such as: -

• 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 1108 is prime or composite. 

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

Step 2: Divide 1108 by 2. It is divisible by 2, so 2 is a factor of 1108. 

Step 3: Divide 1108 by 3. It is not divisible by 3, so 3 is not a factor of 1108. 

Step 4: You can simplify checking divisors by finding the square root of 1108 and checking divisors up to that value. 

Step 5: Continue checking divisibility by other numbers: 1108 is divisible by 4, 277, and 554, among others.

Since 1108 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 is 8, which is even, so 1108 is divisible by 2. 

Divisibility by 3: The sum of the digits in the number 1108 is 10. Since 10 is not divisible by 3, 1108 is not divisible by 3. 

Divisibility by 5: The unit’s place digit is not 0 or 5, so 1108 is not divisible by 5. 

Divisibility by 7: Using divisibility rules, 1108 is not divisible by 7. 

Divisibility by 11: The difference between the sum of the digits in odd positions and even positions is 0, which is divisible by 11, so 1108 is divisible by 11.

Since 1108 is divisible by numbers other than 1 and itself, it has more than two factors, making it a composite number.

The prime number chart is a tool created using a method called “The Sieve of Eratosthenes.” In this method, we follow these steps: 

Step 1: Write numbers in a sequence up to a certain range. 

Step 2: Leave 1 without marking, as it is neither prime nor composite. 

Step 3: Mark 2 and cross out all its multiples. 

Step 4: Mark 3 and cross out all its multiples. -

Step 5: Repeat this process for subsequent numbers.

Through this process, you can identify prime numbers within a range.

Since 1108 is not in the list of prime numbers up to its value, it is a composite number.

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

Step 1: We can write 1108 as 2 × 554. 

Step 2: In 2 × 554, 554 is a composite number. Further, break 554 into 2 × 277. 

Step 3: Now we have the product consisting of only prime numbers.

Hence, the prime factorization of 1108 is 2 × 2 × 277.

• Composite numbers: Natural numbers greater than 1 that are divisible by more than 2 numbers are called composite numbers. For example, 1108 is a composite number because it is divisible by several numbers. 
  
   
• Divisibility Test: A set of rules used to determine if one number is divisible by another.
  
   
• Prime Factorization: The process of expressing a number as a product of its prime factors. 
  
   
• Sieve of Eratosthenes: An ancient algorithm used to find all prime numbers up to a specified integer. 
  
   
• Factors: Numbers that divide a given number exactly without leaving a remainder. For example, the factors of 1108 include 1, 2, 4, 277, 554, and 1108.