Is 472 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 472 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 472 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 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 472 is prime or composite.

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

Step 2: Divide 472 by 2. It is divisible by 2, so 2 is a factor of 472.

Step 3: Divide 472 by 3. It is not divisible by 3, so 3 is not a factor of 472.

Step 4: You can simplify checking divisors up to 472 by finding the root value.

We then need to only check divisors up to the root value. Since 472 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 ones' place value is 2. 2 is an even number, which means that 472 is divisible by 2.

Divisibility by 3: The sum of the digits in the number 472 is 13. Since 13 is not divisible by 3, 472 is also not divisible by 3.

Divisibility by 5: The unit’s place digit is 2. Therefore, 472 is not divisible by 5.

Divisibility by 7: The last digit in 472 is 2. To check divisibility by 7, double the last digit (2 × 2 = 4). Then, subtract it from the rest of the number (47 - 4 = 43). Since 43 is not divisible by 7, 472 is also not divisible by 7.

Divisibility by 11: In 472, the sum of the digits in odd positions is 4 + 2 = 6, and the sum of the digits in even positions is 7. The difference is 1, which means that 472 is not divisible by 11. Since 472 is divisible only by 2, 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 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. 472 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 472 as 2 × 236.
 

Step 2: In 2 × 236, 236 is a composite number. Further, break the 236 into 2 × 118.
 

Step 3: Continue breaking down 118 as 2 × 59.
 

Step 4: Now, we get the product consisting of only prime numbers. Hence, the prime factorization of 472 is 2 × 2 × 2 × 59.

• Composite numbers: Natural numbers greater than 1 that are divisible by more than 2 numbers are called composite numbers. For example, 472 is a composite number because it is divisible by 1, 2, 4, 8, 59, 118, 236, and 472.
   
• Prime numbers: Numbers greater than 1 that have only 2 factors, 1 and themselves, are called prime numbers. For example, 59 is a prime number because it is divisible only by 1 and 59.
   
• Factors: The numbers that divide the number exactly without leaving a remainder are called factors. For example, the factors of 8 are 1, 2, 4, and 8 because they divide 8 completely.
   
• Divisibility: A number is divisible by another if it can be divided evenly without leaving a remainder. For example, 472 is divisible by 2 because dividing 472 by 2 gives a whole number.
   
• Prime factorization: The process of breaking down a number into its prime factors is called prime factorization. For example, the prime factorization of 472 is 2 × 2 × 2 × 59.