Is 479 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 479 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 479 has no divisors other than 1 and 479, it is a prime number.
   
• Several methods can be used to distinguish between prime and composite numbers.
   

These methods include:

• 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 numbers as prime or composite.

• 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 479 is prime or composite.
 

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

Step 2: Divide 479 by numbers starting from 2 up to the square root of 479.
 

Step 3: Since 479 is not divisible by any number other than 1 and itself, it confirms that 479 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: 479 is an odd number, so it is not divisible by 2.

Divisibility by 3: The sum of the digits of 479 is 20, which is not divisible by 3.
 

Divisibility by 5: The unit’s place digit is 9, so 479 is not divisible by 5.
 

Divisibility by 7: The last digit in 479 is 9. To check divisibility by 7, double the last digit (9 × 2 = 18). Subtract it from the rest of the number (47 - 18 = 29). Since 29 is not divisible by 7, 479 is also not divisible by 7.
 

Divisibility by 11: In 479, the sum of the digits in odd positions is 13, and the sum of the digits in even positions is 7. The difference is 6, which is not divisible by 11.

Since 479 is not divisible by any of these, it remains 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 steps below:

Step 1: Write numbers in a range, for example, 1 to 500.

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 end of the list. Through this process, we will have a list of prime numbers within the range.

Since 479 is not crossed out in this 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 write 479 as a product of smaller numbers.

Step 2: Check divisibility by smaller prime numbers such as 2, 3, 5, 7, 11, etc.

Step 3: Since 479 is only divisible by 1 and 479 itself, it cannot be broken down further into other prime numbers, confirming 479 as a prime number.

• Prime numbers: Natural numbers greater than 1 that have no divisors other than 1 and itself.
   
• Composite numbers: Natural numbers greater than 1 that have more than two distinct positive divisors.
   
• Divisibility test: A set of rules to determine whether a number is divisible by another number without performing division.
   
• Prime factorization: The expression of a number as the product of its prime factors.
   
• Sieve of Eratosthenes: An ancient algorithm used to find all prime numbers up to a specified integer.