Is 476 a Prime Number?

There are two main types of numbers: 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 have 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 numbers because they have only one common factor, which is 1.

As 476 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 476 has more than two factors, it is not a prime number.

Several methods are used to distinguish between prime and composite numbers.

A few methods include:

• 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 as prime or composite.

• 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 476 is prime or composite.
 

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

Step 2: Divide 476 by 2. It is divisible by 2, so 2 is a factor of 476.
 

Step 3: Divide 476 by 3. It is not divisible by 3, so 3 is not a factor of 476.
 

Step 4: You can simplify checking divisors up to 476 by finding the square root value. We then need to check divisors up to the square root value.
 

Step 5: When we divide 476 by 2, 4, etc., it is divisible by several numbers. Since 476 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 is 6, which is even, meaning 476 is divisible by 2.
 

Divisibility by 3: The sum of the digits in 476 is 17. Since 17 is not divisible by 3, 476 is not divisible by 3.
 

Divisibility by 5: The unit’s place digit is not 0 or 5, so 476 is not divisible by 5. - Divisibility by 7, 11: Further divisibility tests reveal that 476 does not meet these criteria. Since 476 is divisible by numbers other than 1 and itself, it has more than two factors, making it a composite number.
 

The prime number chart is a tool created 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. Since 476 is not present in the list of prime numbers (and clearly exceeds this list), it is a composite number.
 

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

Step 1: We can write 476 as 2 × 238.
 

Step 2: In 2 × 238, 238 is a composite number. Further, break 238 into 2 × 119.
 

Step 3: Break 119 into 7 × 17. Now we get the product consisting of only prime numbers. Hence, the prime factorization of 476 is 2 × 2 × 7 × 17.

• Prime numbers: Natural numbers greater than 1 that have no divisors other than 1 and themselves. For example, 11 is a prime number.
   
• Composite numbers: Natural numbers greater than 1 that are divisible by more than two numbers. For example, 12 is a composite number because it is divisible by 1, 2, 3, 4, 6, and 12.
   
• Divisibility: A number's capacity to be divided by another number without leaving a remainder. For example, 10 is divisible by 5.
   
• Prime factorization: Breaking down a number into its prime factors. For instance, the prime factorization of 18 is 2 × 3 × 3.
   
• Sieve of Eratosthenes: A method used to find all prime numbers up to a specified integer by repeatedly marking the multiples of each prime number.