Is 477 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 477 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 477 has more than two factors, it is not a prime number. A few methods are used to distinguish between prime and composite numbers.

Some of these 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 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 477 is prime or composite.

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

Step 2: Divide 477 by 2. It is not divisible by 2, so 2 is not a factor of 477.

Step 3: Divide 477 by 3. It is divisible by 3, so 3 is a factor of 477.

Step 4: You can simplify checking divisors up to 477 by finding the square root value. We then need to only check divisors up to the square root value. Step 5: When we divide 477 by 3 and other numbers up to its square root, it is divisible by 3, 9, and other numbers. Since 477 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: The number in the one's place value is 7, which is odd, so 477 is not divisible by 2.
 

Divisibility by 3: The sum of the digits in the number 477 is 18. Since 18 is divisible by 3, 477 is also divisible by 3.
 

Divisibility by 5: The unit’s place digit is 7, which is not 0 or 5, so 477 is not divisible by 5.
 

Divisibility by 7: The last digit in 477 is 7. To check divisibility by 7, double the last digit (7 × 2 = 14). Then, subtract it from the rest of the number (47 - 14 = 33). Since 33 is divisible by 7, 477 is also divisible by 7.
 

Divisibility by 11: In 477, the sum of the digits in odd positions (4 and 7) is 11, and the digit in even position (7) is 7. The difference is 4, which is not divisible by 11, so 477 is not divisible by 11. Since 477 is divisible by numbers other than 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 the following steps.

Step 1: Write numbers 1 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 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 500. If 477 is not present in the list of prime numbers, 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 477 as 3 × 159.

Step 2: In 3 × 159, 159 is a composite number. Further, break 159 into 3 × 53.

Step 3: Now we get the product consisting of only prime numbers. Hence, the prime factorization of 477 is 3 × 3 × 53.

• 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.
   
• Prime factorization: The process of breaking down a composite number into prime numbers.
   
• Divisibility rules: A set of rules that help determine if one number is divisible by another without performing division.
   
• Sieve of Eratosthenes: An ancient algorithm used to find all prime numbers up to a specified integer.
   
• Co-prime numbers: Two numbers that have only 1 as their common factor. For example, 8 and 15 are co-prime.