Is 496 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.

As 496 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 496 has more than two factors, it is not a prime number. A few methods are used to distinguish between prime and composite numbers, such as: 

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

The method in which we count the number of divisors to categorize 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 496 is prime or composite.

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

Step 2: Divide 496 by 2. It is divisible by 2, so 2 is a factor of 496.

Step 3: Divide 496 by 3. It is not divisible by 3, so 3 is not a factor of 496.

Step 4: You can simplify checking divisors up to 496 by finding the root value. We then need to check divisors only up to the root value.

Step 5: When we divide 496 by 2, 4, 8, and 16, it is divisible by these numbers.

Since 496 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. Six is an even number, which means that 496 is divisible by 2. 

Divisibility by 3: The sum of the digits in the number 496 is 19. Since 19 is not divisible by 3, 496 is also not divisible by 3. 

Divisibility by 5: The unit’s place digit is 6. Therefore, 496 is not divisible by 5. 

Divisibility by 7: Using the divisibility rule of 7, 496 is not divisible by 7. 

Divisibility by 11: In 496, the alternating sum of the digits is 11. Since 11 is not divisible by 11, 496 is not divisible by 11. Since 496 is divisible by more than just 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.

Since 496 is not present in the list of prime numbers, it is a composite number.

Prime factorization is the process of breaking down a number into prime factors. Then, multiply those factors to obtain the original number.

Step 1: We can write 496 as 2 × 248.

Step 2: In 2 × 248, 248 is a composite number. Further, break the 248 into 2 × 124.

Step 3: Further break down 124 into 2 × 62. Step 4: Break down 62 into 2 × 31, where 31 is a prime number.

Hence, the prime factorization of 496 is 2 × 2 × 2 × 2 × 31.

• Prime Numbers: Natural numbers greater than 1 that are divisible only by 1 and themselves. For example, 7 is a prime number.

• Composite Numbers: Natural numbers greater than 1 that are divisible by more than 2 numbers. For example, 12 is a composite number.

• Factors: Numbers that divide a given number exactly without leaving a remainder. For example, the factors of 10 are 1, 2, 5, and 10.

• Divisibility Test: A method used to 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. For example, the prime factorization of 18 is 2 × 3 × 3.