Is 1087 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 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 1087 has only two factors, it is a prime number.

The characteristic of a prime number is that it has only two divisors: 1 and itself. Since 1087 meets this criterion, it is a prime number. 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 1087 is prime or composite.

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

Step 2: Check divisibility by numbers up to the square root of 1087, which is approximately 33.

Step 3: 1087 is not divisible by any number from 2 to 33.

Since 1087 has only 2 divisors, it is a prime 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: 1087 is odd, so it is not divisible by 2.

Divisibility by 3: The sum of the digits in 1087 is 16. Since 16 is not divisible by 3, 1087 is also not divisible by 3.

Divisibility by 5: The unit’s place digit is 7. Therefore, 1087 is not divisible by 5.

Divisibility by 7, 11, etc., up to 33: None of these numbers divide 1087 exactly. Since 1087 is not divisible by any number other than 1 and itself, it is a prime 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 numbers in a sequence starting from 1.

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: Continue marking the next available number as prime and crossing out its multiples.

Through this process, we can generate a list of prime numbers. 1087 is not eliminated in this process, confirming it as a prime 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: Check divisibility of 1087 by any prime number up to its square root (approximately 33).

Step 2: 1087 is not divisible by any prime numbers, so it cannot be broken down further.

Hence, 1087 is a prime number because it cannot be factored further into other numbers except by 1 and itself.

• Prime numbers: Natural numbers greater than 1 that are divisible only by 1 and themselves.
   
• Composite numbers: Numbers that have more than two distinct positive divisors.
   
• Factors: Numbers that divide another number exactly without leaving a remainder.
   
• Divisibility test: A method to 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.