The Easy way to Identify Prime and Composite Numbers

Prime and composite numbers

As a mathematics enthusiast, I have encountered many individuals needing help differentiating between prime and composite numbers. In this comprehensive guide, I will take you through everything you need to know about identifying prime and composite numbers. From the basic definitions to tips and tricks and even some common misconceptions, you will find all the information you need to master this topic.

Introduction to Prime and Composite Numbers

In mathematics, numbers can be broadly classified into two categories; prime numbers and composite numbers. These two terms may sound familiar, but what exactly do they mean?

What are Prime Numbers?

A prime number can be defined as an integer bigger than one with only 1 and numbers itself in its factors.

Simply, we can say that a prime number can be divided by one and itself only.

For instance, $$2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, $$ and $$97$$ are all prime numbers.

Examples of Prime Numbers

To better understand prime numbers, let us look at some examples.  Only 1 and 7 are the two factors when we find factors of 7.  Therefore, 7 is a prime number. 

Another example is 23, as only 1 and 23 divide it. Therefore, 23 is also a prime number.

What are Composite Numbers?

A composite number is a positive integer greater than one with more than two positive divisors. In simpler terms, it is a number that can be divided by more than just one and itself. 

For instance, $$4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, $$

$$39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, $$

$$75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, $$ and $$99$$  are all composite numbers.

Examples of Composite Numbers

Let us take the number 6, for instance. When we factorize six into its factors we get  1, 2, 3, and 6. Therefore, it is a composite number. 

Another example is 15, which can factorize into 1, 3, 5, and 15. So its has a factor other than 1 and itself so, it is also a composite number.

Identifying a Number as Prime or Composite

How do we tell if a number is prime or composite now that we understand prime and composite numbers? There are a few techniques that can make it simple for you to distinguish between prime and composite numbers.

Christmas Tree Prime and Composite Worksheet Prime and Composite Worksheet Prime and Composite Worksheet is a great way

Tips and Tricks for Identifying Prime and Composite Numbers


The Number 1

One is not a prime number because it has no divisor other than itself.

The number one is neither a prime nor a composite.


Even Numbers

The only even prime number is 2. While all other even numbers are categorized as composite number,



A number is a prime number if only divisible by 1 and itself. A composite number, on the other hand, is divisible by more than just 1 and itself.


Prime Factorization

To identify a number’s prime factors, use the prime factorization technique. It is a prime number if a number only has two elements. A number is a composite number if there are more than two elements.


Square Roots

The square root of a prime number is irrational, while the square root of a composite number is rational.

Common Misconceptions about Prime and Composite Numbers

A few common things about prime and composite numbers could be improved. One of the most common is that 1 is a prime number. 

Another misconception is that all odd numbers are prime numbers. But, there are many odd composite numbers. For instance, 9, 15, and 21 are all composite numbers.

Prime or Composite Numbers / Examples for Practice

Now that we have covered the basics, let us put our knowledge to the test. Here are a few examples of numbers, and you can determine whether they are prime or composite:


Is 2 a Composite Number? - Explanation and Reasoning

No, 2 is not a composite number. It is a prime number as only 1 and 2 are its factors.


Is 21 Prime or Composite? - Explanation and Reasoning

21 is a composite number because it is divisible by 1, 3, 7, and 21.


Is 13 Prime or Composite? - Explanation and Reasoning

13 is a prime number because it has only two factors 1 and 13.


Is 9 Prime or Composite? - Explanation and Reasoning

9 is a composite number because when we factorize it, we get three factors, 1,3, and 9.


Is 11 Prime or Composite? - Explanation and Reasoning

11 is a prime number as 1 and 11 are its only two factors.


Is 15 Prime or Composite? - Explanation and Reasoning

15 is a composite number because it can be factorized into more than two factors 1, 3, 5, and 15.

Online Resources for Prime and composite numbers Practice Problems

Primes and composites are basic notions of mathematics that underpin most of the advanced mathematical studies. In order to do well mathematics, students have to understand these topics very well. Despite this, the concepts are quite challenging for some students. Fortunately, there are lots of online resources like that allow students to exercise on primes and composites.

Khan Academy
  • One of the best web sites for solving online prime and composite numbers problems is Khan Academy. 
  • Solve the task to see that students practice identifying prime and composite numbers, finding factors, and understanding the properties of prime numbers. 
  • The site gives a more comprehensive coverage and also each concept is explained thoroughly and further more it teaches and gives step-by-step approach for understanding better.
Math Playgrounds
  • The Math Playground is another useful online resource for solving prime and composite number problems. 
  • By using an array of interactive games as well as activities students can train their skills of recognising prime and composite numbers, finding factors and getting acquainted with the concept of prime numbers.
  • The games are very interactive and amusing, hence, students can learn concepts with ease.
Cool Math 
  • One more online source for number games about composite and prime numbers is Cool Math. The website provides a variety of engaging activities, games, and problems that allow learners to enhance their prime and composite counting skills, determine factors, and learn the characteristics of prime numbers. 
  • Besides, the platform supplies extended explanations and organized answers that allow students to grasp the ideas deeper.

Online resources are a great opportunity for students to get problems related to prime and composite numbers without having to open a book. One can visit Khan Academy, Math Playground, and Cool Math; they are just some of the numerous online resources that can help one learn these concepts. Through these resources, students can improve their mastery of prime and composite numbers with regular practice, and thus, obtain a better performance in mathematics.


Conclusion and Summary of Key Takeaways

Mathematics contains prime and composite numbers as articles of great importance. Unlike composite numbers, which can be divided by numbers greater than 1, prime numbers can be divided only by 1 and the number itself. Through the strategies we’ve demonstrated, it is easy to differentiate prime numbers from composite numbers. Remember that 1 is neither prime nor composite. Moreover, all even numbers greater than 2 are composite. 

Here are the main ideas to remember from this tutorial, in brief: Here are the main ideas to remember from this tutorial, in brief:

  • A number which can only be divided by one and itself is regarded to be a prime number.
  • A number which can be divided by a number other than 1, is called a composite number.
  • Composite numbers or even numbers greater than 2.
  • The process is known as the prime factorization of a number to find the prime factors of it.
  • Not every odd number is always a prime number.
  • Not number one either composite or prime.

You should be now able to see difference between prime and composite numbers after knowing about this. So, check out the examples that we have provided as it is essential.


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