Is 490 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 have a few properties:
 

• 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 490 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 490 has more than two factors, it is not a prime number.
   
• A few methods are 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 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 490 is prime or composite.
   

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

Step 2: Divide 490 by 2. It is divisible by 2, so 2 is a factor of 490.

Step 3: Divide 490 by 3. It is not divisible by 3, so 3 is not a factor of 490.

Step 4: You can simplify checking divisors up to 490 by finding the square root value. We then need to only check divisors up to this root value.

Since 490 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 0, which is an even number, meaning that 490 is divisible by 2.
 

Divisibility by 3: The sum of the digits in the number 490 is 13. Since 13 is not divisible by 3, 490 is not divisible by 3.
 

Divisibility by 5: The unit’s place digit is 0. Therefore, 490 is divisible by 5.
 

Divisibility by 7: To check divisibility by 7, double the last digit (0 × 2 = 0) and subtract it from the rest of the number (49 - 0 = 49).

Since 49 is divisible by 7, 490 is also divisible by 7. Since 490 is divisible by numbers other than 1 and itself, it has more than two factors and is 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 a 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. 490 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 multiplying those factors to obtain the original number.

Step 1: We can write 490 as 2 × 245.

Step 2: In 2 × 245, 245 is a composite number. Further, break down 245 into 5 × 49.

Step 3: Break down 49 into 7 × 7.

Step 4: Now we get the product consisting of only prime numbers. Hence, the prime factorization of 490 is 2 × 5 × 7 × 7.

• 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 numbers: Numbers greater than 1 that have no divisors other than 1 and themselves. For example, 13 is a prime number.
   
• Divisibility rules: A set of rules to determine if one number is divisible by another without performing division. For example, a number is divisible by 2 if its last digit is even.
   
• Factors: The numbers that divide a given number exactly without leaving a remainder are called factors. For example, the factors of 4 are 1, 2, and 4.
   
• Prime factorization: The process of expressing a number as the product of its prime factors. For instance, the prime factorization of 18 is 2 × 3 × 3.