What are Composite Numbers?

Composite Numbers Definition

All natural numbers that can be expressed as a product of at least two smaller natural numbers are known as composite numbers.

In other words, a natural number that has at least one factor other than 1 and the number itself is called a composite number.

Composite Numbers Examples

Some initial composite numbers in ascending order are:

4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20,…

Notice that each of these have factor(s) between 1 and the number itself. Like 4 has 2, 6 has 2 & 3 and so on.

Note: All the natural numbers that are not 1 and not prime are composite numbers.

Types of Composite Numbers

• Even Composite Numbers: The numbers that are even and composite. There are infinitely many such numbers like 4, 6, 8, 10, etc.
• Odd Composite Numbers: The numbers that are odd and composite are Odd Composite Numbers. There are infinitely many such numbers like 9, 15, 21, 25, 49, etc.

List of Composite Numbers

Composite Numbers from 1 to 100 are listed below:

List of Composite Numbers from 1 to 100

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, 99, & 100

Facts about Composite Numbers

1. Product of Primes: Every composite number can be expressed as a unique product of prime numbers, known as its prime factorization. This property is a fundamental concept in number theory and plays a crucial role in various mathematical applications, including cryptography.
2. Abundance or Excess: Composite numbers often exhibit an interesting property known as abundance or excess. The abundance of a composite number is the difference between the sum of its proper divisors and the number itself. Abundant numbers have an abundance greater than the number itself, while deficient numbers have an abundance less than the number.
3. Distribution: Composite numbers are abundant in the set of natural numbers. As numbers increase, the proportion of composite numbers to prime numbers also increases significantly.
4. Divisibility Tests: Many divisibility tests, such as those for 2, 3, 4, 5, 6, 8, 9, and 10, can determine if a number is composite without performing actual division. These tests rely on the properties of composite numbers and their divisibility patterns.
5. Role in Cryptography: Composite numbers play a crucial role in modern cryptography, particularly in RSA encryption, where the security of the algorithm depends on the difficulty of factoring large composite numbers into their prime factors.
6. Square Numbers: Many composite numbers are also square numbers, meaning they can be expressed as the square of an integer. Square composite numbers have multiple prime factors that are repeated in their prime factorization.
7. Composite Ciphers: In cryptography, composite numbers are used in the creation of composite ciphers, which employ multiple encryption algorithms or keys to enhance security and resist attacks.
8. Historical Significance: Throughout history, the study of composite numbers has contributed to the development of various mathematical concepts, algorithms, and encryption techniques, making them essential in both theoretical and practical domains of mathematics and computer science.

Prime and Composite Numbers are commonly used classifications of Natural Numbers based on divisibility and the number of Factors. A Prime Number has only two factors while Composite Numbers have more than two factors. This classification of Numbers makes the study of natural numbers more organized and convenient and is useful in a variety of situations like computer algorithms, biology, understanding of Number Theory, etc.

This article describes what are prime and composite numbers, the types of primes and composite numbers, and tests to check whether a given number is prime or not (primality tests). Finally, a few solved questions, and a few practice problems related to prime and composite numbers are presented.