Is 1088 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 because they have only one common factor, which is 1.
   
• As 1088 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 1088 has more than two factors, it is not a prime number. A few methods are used to distinguish between prime and composite numbers: 

• 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 1088 is prime or composite.

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

Step 2: Divide 1088 by 2. It is divisible by 2, so 2 is a factor of 1088.

Step 3: Divide 1088 by 3. It is not divisible by 3, so 3 is not a factor of 1088.

Step 4: You can simplify checking divisors up to 1088 by finding the square root. We then need to only check divisors up to the root value.

Since 1088 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 8, which is even, so 1088 is divisible by 2. 

Divisibility by 3: The sum of the digits in the number 1088 is 17. Since 17 is not divisible by 3, 1088 is also not divisible by 3. 

Divisibility by 5: The unit’s place digit is 8. Therefore, 1088 is not divisible by 5.

Divisibility by 11: The alternating sum of the digits is 1 - 0 + 8 - 8 = 1, which is not divisible by 11.

Since 1088 is divisible by 2, 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. 1088 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. Then multiply those factors to obtain the original number.

Step 1: We can write 1088 as 2 × 544.

Step 2: In 2 × 544, 544 is a composite number. Further, break the 544 into 2 × 272.

Step 3: Continue the process: 272 = 2 × 136, and 136 = 2 × 68, then 68 = 2 × 34, and finally 34 = 2 × 17.

Hence, the prime factorization of 1088 is 2 × 2 × 2 × 2 × 2 × 2 × 17 (or 2^6 × 17).

• Composite numbers: Natural numbers greater than 1 that are divisible by more than 2 numbers are called composite numbers. For example, 1088 is a composite number because it has multiple divisors. 
   
• Divisibility rules: A set of rules that help determine if one number is divisible by another without performing division. 
   
• Prime factorization: The process of expressing a number as the product of its prime factors. 
   
• Sieve of Eratosthenes: An ancient algorithm used to find all prime numbers up to a specified integer. 
   
• Co-prime numbers: Two numbers that have only 1 as their common factor.