Is 486 a Prime Number?

Numbers are categorized into two types based on the number of factors: prime numbers and composite numbers.

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, 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 because their only common factor is 1.
   

As 486 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 486 has more than two factors, it is not a prime number.

There are a few methods to distinguish between prime and composite numbers:

• Counting Divisors Method
   
• Divisibility Test
   
• Prime Number Chart
   
• Prime Factorization
   

The counting divisors method involves counting the number of divisors to categorize numbers as prime or composite.

Based on the count of divisors, we categorize numbers:

• If there are only 2 divisors, then the number is prime.
   
• If the count is more than 2, then the number is composite.
   

Let’s check whether 486 is prime or composite.

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

Step 2: Divide 486 by 2. It is divisible by 2, so 2 is a factor of 486.

Step 3: Divide 486 by 3. It is divisible by 3, so 3 is a factor of 486.

Step 4: You can simplify checking divisors up to 486 by finding the square root value. We then need to only check divisors up to the square root.

Step 5: When we divide 486 by 2, 3, and other numbers up to its square root, it is divisible by several numbers.

Since 486 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 6, an even number, which means that 486 is divisible by 2.

Divisibility by 3: The sum of the digits in the number 486 is 18 (4 + 8 + 6 = 18). Since 18 is divisible by 3, 486 is also divisible by 3.

Divisibility by 5: The unit’s place digit is 6, which is not 0 or 5, so 486 is not divisible by 5.

Divisibility by 7: Using the rule for 7, 486 is not divisible by 7 since the calculations do not result in a multiple of 7.

Divisibility by 11: Alternating sum of digits in 486 (4 - 8 + 6) is 2, which is not divisible by 11.

Since 486 is divisible by numbers other than 1 and itself, 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 these steps:

Step 1: Write numbers from 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 from 1 to 100.

The list is 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97.

486 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 its prime factors.

Then multiply those factors to obtain the original number.

Step 1: We can write 486 as 2 × 243.

Step 2: 243 is a composite number. Further, break down 243 into 3 × 81.

Step 3: 81 is a composite number. Further, break down 81 into 3 × 27.

Step 4: 27 is a composite number. Further, break down 27 into 3 × 9.

Step 5: 9 is a composite number. Further, break down 9 into 3 × 3.

Step 6: Now we get the product consisting of only prime numbers.

Hence, the prime factorization of 486 is 2 × 3 × 3 × 3 × 3 × 3.

• Composite numbers: Natural numbers greater than 1 that are divisible by more than 2 numbers. For example, 12 is a composite number because 12 is divisible by 1, 2, 3, 4, 6, and 12.
   
• Prime factorization: The process of expressing a composite number as a product of its prime factors.
   
• Divisibility test: A set of rules 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.
   
• Co-prime numbers: Two numbers are co-prime if their greatest common divisor is 1.