Is 487 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.

Since 487 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 487 has only two factors, 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 487 is prime or composite.

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

Step 2: Check divisibility by other numbers up to the square root of 487, which is approximately 22. - 487 is not divisible by 2, 3, 5, 7, 11, 13, 17, or 19.

Since 487 has only 2 divisors, 1 and 487, 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: 487 is odd, so it is not divisible by 2.
 

Divisibility by 3: The sum of the digits in 487 is 19, which is not  divisible by 3.
 

Divisibility by 5: The last digit is not 0 or 5, so it is not divisible by 5.
 

Divisibility by 7: Using divisibility rules, 487 is not divisible by 7.
 

Divisibility by 11: The alternating sum of the digits in 487 is 9, which is not divisible by 11.

Since 487 is not divisible by any of these numbers, it has only two factors, 1 and 487, making it 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 grid up to a certain limit.

Step 2: Leave 1 without marking, 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 for prime candidates until reaching the necessary limit.

Through this process, we identify prime numbers.

Since 487 is not crossed out in the list, it is confirmed 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: Attempt to divide 487 by the smallest prime numbers (2, 3, 5, 7, 11, 13, 17, 19).

Step 2: 487 is not divisible by any of these primes. Since 487 cannot be factored into smaller prime numbers, it is itself a prime number.

• Prime numbers: Natural numbers greater than 1 that are divisible only by 1 and themselves.
   
• Composite numbers: Natural numbers greater than 1 that are divisible by more than 2 numbers.
   
• Divisibility rules: Guidelines to determine whether a number is divisible by another number without performing full 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.