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 603 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 603 has more than two factors, it is not a prime number. A few methods are used to distinguish between prime and composite numbers: 

• 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 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 603 is prime or composite. 

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

Step 2: Divide 603 by 2. It is not divisible by 2, so 2 is not a factor of 603.

Step 3: Divide 603 by 3. It is divisible by 3, so 3 is a factor of 603.

Step 4: You can simplify checking divisors up to 603 by finding the square root value. We then need to only check divisors up to this square root value.

Since 603 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 3, which is odd, so 603 is not divisible by 2.

Divisibility by 3: The sum of the digits in the number 603 is 9. Since 9 is divisible by 3, 603 is also divisible by 3. 

Divisibility by 5: The unit’s place digit is 3. Therefore, 603 is not divisible by 5. 

Divisibility by 7: To check divisibility by 7, double the last digit (3 × 2 = 6). Then, subtract it from the rest of the number (60 - 6 = 54).

Since 54 is divisible by 7, 603 is also divisible by 7. Since 603 is divisible by 3 and 7, 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 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.

Since 603 is not in this list, and it is divisible by numbers other than 1 and itself, 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 603 as 3 × 201. 

Step 2: In 3 × 201, 201 is a composite number. Further, break 201 into 3 × 67. 

Step 3: Now we get the product consisting of only prime numbers.

Hence, the prime factorization of 603 is 3 × 3 × 67.

• 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 itself.

• Divisibility: A number is divisible by another when it can be divided without leaving a remainder.

• Prime factorization: The process of expressing a number as the product of its prime factors.

• Co-prime numbers: Two numbers are co-prime if their greatest common divisor is 1.