Last updated on July 4th, 2025
Numbers are classified into different types based on their properties. Composite numbers are the numbers with more than two factors. In this topic, we will learn about the concepts of composite numbers.
Numbers are of two types based on how many factors they have, prime and composite numbers. Composite numbers are the numbers that have more than two factors. Composite numbers are divisible by more than two integers. For instance, 8 is a composite number, as 1, 2, 4, and 8 are the factors of 8. The smallest composite number is 4 because 1, 2, and 3 are only divisible by 1 and the number itself. These natural numbers have more than two factors. Furthermore, if a number has only 2 factors, 1 and the same number, it is called a prime number.
By looking at the history of composite numbers, we can understand the development and relationship of numbers. For beneficial reasons, such as trade, measurements, and documentation, numbers were recognized by ancient civilizations like the Mesopotamians and Egyptians. Mesopotamians and Egyptians used numbers, but they were not the pioneers in defining composite numbers. In Ancient Greece, Pythagoreans classified numbers into even, odd, prime, and composite according to the nature of the numbers. Around 300 BCE, Euclid introduced the first official explanation for composite numbers. He stated that these numbers can be defined as the product of two small numbers.
During the 16th and 17th centuries, Leonhard Euler introduced significant theorems about primes, composites, and divisors. Nowadays, modern cryptography relies on composite numbers to simplify processes when working with huge numbers and prime factorization.
The numbers with more than 2 factors are composite. Composite numbers are the products of their prime factors as well. Here, are a few properties of composite numbers:
Small integers, whether they are prime or composite, can completely divide a composite number.
A composite number can be divided precisely in a variety of ways. Composite numbers are classified by how many factors a number possesses and its characteristics. Composite numbers are greater than 1. They have more than two independent factors; also, they can be divided evenly by numbers other than 1 and themselves. In the fields of cryptography, number theory, and factorization, composite numbers are essential.
Even composite numbers
The first category of composite numbers is even composite numbers. It is possible to divide even composite numbers by 2. For example, 4, 6, 8,… 60, 78, etc. are some examples of even composite numbers. These numbers have more than two factors. For instance, the factors for the number 66 are 1, 2, 3, 6, 11, 22, 33, and 66.
Odd composite numbers
The next one is odd composite numbers. These numbers cannot be divided by 2. The numbers such as 9, 15, 21, and 25 are some of the few examples of these numbers. Additionally, these natural numbers include more than two factors.
Square composite numbers
Square composite numbers are perfect squares that are also composite, like 4, 9, 16. These are a specific type of square numbers, which are the product of multiplying a number by itself.
For example, 4, 9, 16, 25, and 36 are some examples of square composite numbers.
Non-Examples of Composite Numbers
Non-composite numbers are the numbers that are not composite and do not have more than two factors. They are the prime numbers, 1 and 0.
Prime numbers are greater than 1; these natural numbers are divisible only by 1 and the number itself. The number 1 is not a prime or composite number because it only has one divisor, that is 1 itself. Zero is not a composite number because zero has an infinite number of divisors.
Examples of Composite Numbers
Examples of composite numbers help us to understand the concept much more easily. These numbers have more than 2 factors, and they are larger than 1.
The first 10 even composite numbers are: 4, 6, 8, 10, 12, 14, 16, 18…
The first 10 odd composite numbers are: 9, 15, 21, 25, 27, 33, 35, 39, 45, 49…
The first 10 square composite numbers are: 4, 9, 16, 25, 36, 49, 64, 81, 100, 121…
Non-Examples of Composite Numbers
Understanding the non-composite numbers enables us to develop a deep understanding of the essential components of the topic.
The first few prime numbers, which are non-examples of composite numbers are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29…
Composite numbers are a vital cornerstone of mathematical comprehension. Students can concentrate on advanced math if they have a stronger grasp of composite numbers. It aids in their understanding of number theory concepts. Composite numbers are essential for doing prime factorization and solving difficult mathematical calculations. Learning the rules of division also requires an understanding of composite numbers.
Identifying composite numbers from a sequence is sometimes tricky. Here are some of the tips and tricks to figure out the composite numbers:
Use divisibility rules: When we determine the factors of a larger number, we follow divisibility rules. If a number is even, then the number is divisible by 2. Also, if the last digit of a number is 0 or 5, then the number is divisible by 5.
Find the small prime numbers: If a number has more than two factors, then the number is a composite. Similarly, a number is considered prime if it contains just two factors.
Apply prime factorization: Prime factorization is a process of dividing a number into its factors. If a number has factors other than 1 and itself, we can consider it a composite number.
Remember the smallest composite number: Always remember that 4 is the smallest composite number. 1 is neither a composite nor a prime number. 2 and 3 are prime numbers. The next digit is 4, and has multiple factors.
Students may also make several common errors while dealing with composite numbers. Here are some common mistakes and their solutions. Avoiding these errors will help students make accurate calculations.
Composite numbers are essential to many sectors. It includes everything from music and entertainment to security procedures and encryption. Composite numbers and their characteristics are crucial for securing online transactions and communications. To determine the dimensions and units related to the buildings and the arrangement of products we use composite numbers. To plan and arrange events systematically, composite numbers are helpful. In music theory, the structure of beats and rhythmic constructions rely on composite numbers. Composite numbers have an infinite number of practical uses.
Check if 105 is a composite number.
Yes. 105 is a composite number.
First, we need to check the factors of 105. If this number has more than two factors, we can consider it as a composite number.
105 is divisible by 1, 3, 5, 7, 15, 21, 35, and 105.
For example,
105 ÷ 3 = 35
105 ÷ 5 = 21
105 has more than 2 factors. Hence, it is a composite number.
Check the sum of two composite numbers, 14 and 36 are composite.
14 and 36 are composite. Their sum is 50. It is also a composite number.
When we add both composite numbers:
14 + 36 = 50
Next, we have to find out whether 50 is a composite number or not.
Since 50 has multiple factors such as 1, 2, 5, 10, 25, and 50, it is a composite number.
Is 101 a composite number or not?
No, 101 is not a composite number because it is only divisible by 1 and 101.
101 is a prime number. It is greater than 1 and has only divisors as 1 and itself.
101 × 1 = 101
Galton has 12 chocolates. He wants to give them to his friends in equal amounts. How can he do this?
To find the answer, we need to find the factors of 12.
The factor of 12 includes 1, 2, 3, 4, 6, and 12.
So, Galton has only one friend, he gets 12 chocolates.
Likewise:
Galton can distribute 12 chocolates in different ways to his friends depending on how many friends he has.
Check if 150 is a composite number.
Yes. 150 is a composite number. The factors of 150 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, and 150. Since 150 has more than two factors, it is not a prime number
150 is a composite number. Because these factors can evenly divide 150 without any remainder.