Is 495 a Prime Number?

There are two main types of numbers —

prime numbers and composite numbers, depending on the number of factors they have.

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 3 only.

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 have certain 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 numbers because they have only one common factor, which is 1.

Since 495 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 495 has more than two factors, it is not a prime number. Several methods can be used to distinguish between prime and composite numbers, including:

• 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 the divisors, we categorize numbers: If there is a total count of only 2 divisors, then the number is prime. If the count is more than 2, then the number is composite. Let’s check whether 495 is prime or composite.

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

Step 2: Divide 495 by 2. It is not divisible by 2, so 2 is not a factor.

Step 3: Divide 495 by 3. It is divisible by 3, so 3 is a factor of 495.

Step 4: You can simplify checking divisors up to 495 by finding the square root value. Then, check divisors up to the square root.

Step 5: When we divide 495 by 3, 5, 9, 11, and others, it is divisible by several numbers.

Since 495 has more than 2 divisors, it is a composite number.

The divisibility test method uses a set of rules to check whether a number is completely divisible by another number.

Divisibility by 2: The number in the ones' place is 5. Since 5 is not even, 495 is not divisible by 2.

Divisibility by 3: The sum of the digits in 495 is 18. Since 18 is divisible by 3, 495 is also divisible by 3.

Divisibility by 5: The unit’s place digit is 5. Therefore, 495 is divisible by 5.

Divisibility by 7: To check divisibility by 7, double the last digit (5 × 2 = 10). Subtract it from the rest of the number (49 - 10 = 39). Since 39 is divisible by 7, 495 is also divisible by 7.

Divisibility by 11: In 495, the sum of the digits in odd positions is 9, and the sum of the digits in even positions is 4. The difference is 5, which is not divisible by 11, so 495 is not divisible by 11. Since 495 is divisible by several numbers, it has more than two factors.

Therefore, it is a composite number.

The prime number chart is a tool created using a method called "The Sieve of Eratosthenes." This method involves 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 as a prime number and cross out all multiples of 2.

Step 4: Mark 3 as a prime number and cross out all multiples of 3.

Step 5: Repeat this process until you reach a table consisting of marked and crossed boxes, except for 1. Through this process, we obtain a list of prime numbers.

Since 495 is not in this list, it is a composite number.

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

Step 1: We can write 495 as 5 × 99.

Step 2: In 5 × 99, 99 is a composite number. Further, break down 99 into 3 × 33.

Step 3: Break down 33 into 3 × 11.

Step 4: Now we get the product consisting of only prime numbers.

Hence, the prime factorization of 495 is 3 × 3 × 5 × 11.

• Composite numbers: Natural numbers greater than 1 that are divisible by more than 2 numbers are called composite numbers. For example, 12 is a composite number because it is divisible by 1, 2, 3, 4, 6, and 12.

• Divisibility rules: A set of rules that help determine if one number is divisible by another without performing division. For example, a number is divisible by 3 if the sum of its digits is divisible by 3.

• Prime factorization: The process of expressing a number as the product of its prime factors. For example, the prime factorization of 18 is 2 × 3 × 3.

• Prime numbers: Natural numbers greater than 1 that have only two factors, 1 and themselves. For example, 7 is a prime number.

• Factors: Numbers that divide a number exactly without leaving a remainder are called factors. For example, the factors of 8 are 1, 2, 4, and 8.