Is 481 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 481 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 481 has more than two factors, it is not a prime number.
   
• Few methods are used to distinguish between prime and composite numbers.
   

A few methods are:
 

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

The method in which we count the number of divisors to categorize the 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 481 is prime or composite.

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

Step 2: Check divisibility of 481 by smaller numbers like 2, 3, 5, 7, 11, etc.

Step 3: 481 is not divisible by 2, 3, 5, or 7.

Step 4: Divide 481 by 13 (since 13 is a prime number), and it is divisible, so 13 is a factor of 481.

Since 481 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. It is called the Divisibility Test Method.

Divisibility by 2: 481 is an odd number, meaning it is not divisible by 2.

Divisibility by 3: The sum of the digits in the number 481 is 13. Since 13 is not divisible by 3, 481 is also not divisible by 3.

Divisibility by 5: The unit’s place digit is 1. Therefore, 481 is not divisible by 5.

Divisibility by 7: Check divisibility by 7. 481 divided by 7 does not result in a whole number.

Divisibility by 11: The alternating sum of the digits (4 - 8 + 1 = -3) is not divisible by 11, so 481 is not divisible by 11.

Since 481 is divisible by 13, 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 the following steps.

Step 1: Write numbers up to 500 in rows and 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 the multiples of 2.
 

Step 4: Mark 3 as 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.

481 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 prime factors. Then multiply those factors to obtain the original number.

Step 1: We can write 481 as 13 × 37.

Step 2: Both 13 and 37 are prime numbers.

Step 3: Hence, the prime factorization of 481 is 13 × 37.

• 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 12 is divisible by 1, 2, 3, 4, 6, and 12. 
   
• Prime numbers: Numbers that have only two distinct positive divisors: 1 and itself. For example, 7 is a prime number.
   
• Divisibility: A concept that determines if one number can be evenly divided by another without leaving a remainder.
   
• Prime factorization: Breaking down a composite number into the product of its prime factors. For example, the prime factorization of 20 is 2 × 2 × 5.
   
• Co-prime numbers: Two numbers are co-prime if their greatest common divisor is 1. For example, 8 and 15 are co-prime.