Is 2003 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 that is 1. Since 2003 has only two factors, it is a prime number.

The characteristic of a prime number is that it has only two divisors: 1 and itself. Since 2003 has only two factors, it is 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 2003 is prime or composite.

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

Step 2: Check divisibility by any prime numbers less than the square root of 2003 (approximately 44.7).

Step 3: 2003 is not divisible by any prime number less than 44.7. Since 2003 has only 2 divisors, it is a prime 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: 2003 is odd, so it is not divisible by 2.

Divisibility by 3: The sum of the digits in 2003 is 5. Since 5 is not divisible by 3, 2003 is not divisible by 3.

Divisibility by 5: The unit’s place digit is 3. Therefore, 2003 is not divisible by 5.

Divisibility by 7, 11, and other primes up to 44: 2003 is not divisible by any of these primes. Since 2003 is not divisible by any number other than 1 and itself, it is a prime 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 in a grid format (for instance, 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 desired range. Through this process, prime numbers can be identified. Since 2003 is not divisible by any prime number up to its square root, it is a prime 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: Attempt to divide 2003 by the smallest prime, which is 2. 2003 is odd, so not divisible by 2.

Step 2: Continue testing divisibility with subsequent primes up to the square root of 2003 (approximately 44.7).

Step 3: 2003 is not divisible by any of these primes. Therefore, 2003 cannot be broken down into smaller prime factors, indicating that it is itself a prime number.

• Prime numbers: Natural numbers greater than 1 that have no divisors other than 1 and itself.

• Composite numbers: Natural numbers greater than 1 that are divisible by more than two numbers.

• Divisibility test: A method used to determine whether one number is divisible by another.

• Sieve of Eratosthenes: An ancient algorithm used to find all prime numbers up to a specified integer.

• Factors: Numbers that divide the given number exactly without leaving a remainder.