Is 2013 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 2013 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 2013 has more than two factors, it is not a prime number. A few methods are used to distinguish between prime and composite numbers. Some 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 2013 is prime or composite.

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

Step 2: Divide 2013 by 2. It is not divisible by 2, so 2 is not a factor of 2013.

Step 3: Divide 2013 by 3. The sum of the digits (2 + 0 + 1 + 3 = 6) is divisible by 3, so 3 is a factor of 2013.

Step 4: You can simplify checking divisors up to 2013 by finding the root value. We then need to only check divisors up to the root value.

Step 5: Since 2013 is divisible by 3, it has more than 2 divisors, making it 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. Since 3 is odd, 2013 is not divisible by 2.

Divisibility by 3: The sum of the digits in the number 2013 is 6. Since 6 is divisible by 3, 2013 is divisible by 3.

Divisibility by 5: The unit’s place digit is 3. Therefore, 2013 is not divisible by 5.

Divisibility by 7: Double the last digit (3 × 2 = 6), then subtract it from the rest of the number (201 - 6 = 195). Since 195 is divisible by 7, 2013 is also divisible by 7.

Divisibility by 11: In 2013, the sum of the digits in odd positions is 5, and the sum of the digits in even positions is 1. The difference is 4, which means that 2013 is not divisible by 11. Since 2013 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 2013 is greater than 100, we continue checking divisibility with prime numbers beyond the list. 2013 is divisible by 3 and 7, confirming it is not 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: We can write 2013 as 3 × 671.

Step 2: In 3 × 671, we check if 671 is a composite number. It turns out that 671 is divisible by 11.

Step 3: Now we get the product consisting of only prime numbers. Hence, the prime factorization of 2013 is 3 × 11 × 61.

• 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.

• Divisibility test: A set of rules to determine if one number is divisible by another without performing the division.

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

• Factors: Numbers that divide the number exactly without leaving a remainder are called factors. For example, the factors of 4 are 1, 2, and 4 because they divide 4 completely.

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