What are Composite Numbers? Definition, Types, List, Chart, Properties, Examples

A composite number is a positive integer that can be formed by multiplying two smaller positive integers. It is also a positive integer that has at least one divisor other than 1 and itself. Composite numbers having a minimum of 3 factors are the opposite of prime numbers, which only have 2 factors.

In this article, we’ll explore composite numbers from 1 to 1000, their significance, definition, and examples. We’ll also study the various types of composite numbers, examine the distinctions between prime and composite numbers, and learn methods for identifying whether a number is composite or not.

What are Composite Numbers?

Natural numbers are categorized as prime numbers, whole numbers, complex numbers, rational numbers, and so on. One of the number categories is a composite number.

In simple words, any natural number is called a composite number if it is not a prime number. Unlike composite numbers, prime numbers only contain two factors: the number itself and 1. Composite numbers are the exact opposite of prime numbers. For example, 6 is a composite number as it may be divided by two, three, or even six. 

Composite Numbers Definition

Numbers with more than two factors are referred to as composite numbers. Composite numbers are those natural numbers that are divisible by more than two numbers or by at least one number other than one and the number itself.

Examples of Composite Numbers

Those are the first few composite numbers: 4, 6, 8, 9, and 10. Using 20 and 22 as examples. Since 20 and 22 in the example above have more than two elements, they are referred to as composite numbers. Now let’s examine some of the crucial characteristics of composite numbers.

First 10 Composite Numbers

As we already discussed, composite numbers are those positive integers greater than 1 that have at least one positive divisor other than 1 and themselves. Here are the first 10 composite numbers:

4	6	8	9	10	12	14	15	16	18

Properties of Composite Numbers

Various properties of composite numbers that are very useful for students are,

• Composite numbers consist of more than two factors.
• Each composite number is one of its own factors.
• Of all composite numbers, 4 is the smallest.
• Composite numbers can be divided evenly by smaller numbers, either prime or composite.
• Divisible by other composite numbers is a composite number.
• At least two prime numbers are factors in every composite number.

Prime Factorization of Composite Numbers

Prime factorization is a process of breaking down a composite number into its prime factors, which are the prime numbers that, when multiplied together, result in the original composite number.

Some examples of prime factorization of composite numbers are:

Prime factorization of 24

• 24 = 2 × 2 × 2 × 3

Prime factorization of 56

• 56 = 2 × 2 × 2 × 7

Prime factorization of 90

• 90 = 2 × 3 × 3 × 5

Prime factorization of 120

• 120 = 2 × 2 × 2 × 3 × 5

Prime factorization of 210

• 210 = 2 × 3 × 5 × 7

Prime factorization of 360

• 360 = 2 × 2 × 2 × 3 × 3 × 5

Composite Numbers From 1 to 1000

As there are 168 prime numbers in the range from 1 to 1000, thus we can find the number of composite number between 1 and 1000 including both the numbers by subtracting 168 from 1000 i.e., 1000 – 168 = 832.

Thus, there are 832 composite numbers between 1 and 1000.

Composite Numbers From 1 to 100

Between 1 and 100, there are 74 composite numbers in total. Below is a list of every composite number 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

Composite Numbers From 101 to 200

Between 101 and 200, there are 74 composite numbers in total. Below is a list of every composite number from 101 to 200.

101	102	104	105	106	108	110	111	112	114	115	116	118	119	120
121	122	123	124	125	126	128	130	132	133	134	135	136	138	140
141	142	144	145	146	147	148	150	152	154	155	156	158	159	160
161	162	164	165	166	168	169	170	172	174	175	176	177	178	180
182	184	185	186	187	188	190	192	194	195	196	198	199	200

Composite Numbers From 201 to 300

From 201 to 300, there are 74 composite numbers in total. Below is a list of every composite number from 201 to 300.

204	206	208	210	212	214	215	216	217	218	219	220	221
222	223	224	225	226	228	230	231	232	234	235	236	238
240	242	243	244	245	246	247	248	249	250	252	254	255
256	258	259	260	261	262	264	265	266	267	268	270	272
273	274	275	276	278	280	282	284	285	286	287	288	290
291	292	294	295	296	297	298	299	300

and so on and on, we can list all the number which are composite.

Composite Number Chart

Following chart provides the all the composite numbers from 1 to 100.

How to Find the Composite Number

Here are the easy steps for calculating the composite numbers:

Step 1: Determine the integer factors that are positive.

Step 2: A number is considered to be a prime number if it has factors such as 1 and the number itself.

Step 3: A composite number is one that includes more than two elements.

Let’s consider an example for better understanding.

Example: Determine whether 16 is a composite number.

Let us look for the elements of 16.

16÷1 = 16

16÷2 = 8

16÷4 = 4

16÷8 = 2

16÷16 = 1

As can be seen, the factors of 16 are 1,2,4,8, and 16, indicating that it is a composite number.

Types of Composite Number

In mathematics, composite numbers come in two primary varieties:

• Even Composite Numbers
• Odd Composite Numbers

Even Composite Numbers

Even composite number refers to a composite number that is also even. Therefore, every even number that isn’t a prime number is also an even composite number. The lowest even composite number is 4.

Examples are 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30. Once more, all of the numbers between 1 and 30 may be found to be even composite numbers. It is possible to determine if they are entirely divisible by two. As you can see, they are even numbers, which is why we referred to them as even composite numbers.

Odd Composite Numbers

Odd composite numbers are those that are composite numbers that are odd. It may alternatively be defined as all odd composite numbers, meaning that all odd integers are not prime numbers. As an odd composite number, 9 is the smallest.

Examples are 9, 15, 21, 25, and 27. The composite numbers that are not divisible by two are those listed here. Thus, these five numbers are odd composite numbers if we take into account all the integers between 1 and 30.

Some Special Composite Numbers

Other than odd and even composite number there are some more special types of composite numbers, some of these types are:

• Smallest Odd Composite Numbers
• Consecutive Composite Numbers
• Highly Composite Numbers

Let’s discuss these types in detail.

Smallest Odd Composite Numbers

The smallest odd composite numbers are integers higher than one that are neither prime nor even. The lowest odd composite number is 9, which may be divided into 3 and 3. 15, 21, and 25 are some such instances. Because they may be written as the product of two or more prime integers, these numbers are intriguing in mathematics.

Consecutive Composite Numbers

A succession of integers bigger than one with more than two divisors is referred to as a consecutive composite number. This indicates they have at least three positive integer factors. For example, the composite numbers 4, 6, and 8 are successive because they can be represented as the product of smaller positive integers. The study of sequential composite numbers is significant in number theory because it gives information on the distribution and features of non-prime numbers.

Highly Composite Numbers

Highly composite numbers are one-of-a-kind integers with more divisors than any smaller positive integer. In other words, they have a disproportionately large number of components in comparison to numbers smaller than themselves. The number 12 is an example of a highly composite number since it contains divisors 1, 2, 3, 4, 6, and 12. Because of their fascinating features and applications, extremely composite numbers are important in a variety of domains, including number theory and cryptography. These numbers are critical in comprehending the behaviour of factors in the domain of integers.

Numbers That are Neither Prime Nor Composite

The number 1 is neither composite nor prime. Prime numbers are natural numbers bigger than one with just two different divisors: one and themselves. Because 1 has only one divisor (itself), it does not meet the requirements for a prime number. Furthermore, because 1 has no more than two divisors, it is not categorised as a composite number. It is more commonly referred to as a “unit” in mathematics.

Divisibility Tests for Composite Numbers

Divisibility tests are algorithms or rules used to determine whether a given number is divisible by another without performing actual division. These tests rely on the properties of numbers, including their factors and digits, to ascertain divisibility efficiently. Composite numbers are central to the development and application of divisibility tests due to their diverse factorization patterns and divisibility properties.

Some commonly used divisibility tests involving composite numbers include:

• Divisibility by 2: A number is divisible by 2 if its last digit is even, indicating that it is composite.
• Divisibility by 3: To test for divisibility by 3, the sum of the digits of the number is computed. If the sum is divisible by 3, then the number itself is divisible by 3, suggesting it is composite.
• Divisibility by 4: A number is divisible by 4 if the last two digits form a number that is divisible by 4, indicating composite nature.
• Divisibility by 5: A number is divisible by 5 if its last digit is 0 or 5, signifying composite properties.
• Divisibility by 6: A number is divisible by 6 if it is divisible by both 2 and 3, indicating composite characteristics.
• Divisibility by 9: Similar to divisibility by 3, the sum of the digits of the number is calculated. If the sum is divisible by 9, then the number itself is divisible by 9, suggesting composite nature.
• Divisibility by 10: A number is divisible by 10 if its last digit is 0, indicating composite properties.

These divisibility tests, along with others for prime numbers and larger divisors, provide efficient means of determining divisibility and identifying composite numbers.

Difference Between Prime and Composite Numbers

Prime Numbers and Composite Numbers

Prime Numbers are natural numbers higher than one with just two different divisors: the number itself and 1. Prime numbers include 2, 3, 5, 7, 11, and 13 since their only divisors are 1 and the number itself.

Composite Numbers, on the other hand, are natural numbers bigger than one that have more than two different divisors. For example, 4, 6, 8, 9, and 12 are composite numbers because they have divisors other than 1 and the number itself.

The main distinguishing features between prime number and composite numbers are listed in the following table:

Prime Numbers Vs Composite Numbers
Characteristic	Prime Numbers	Composite Numbers
Definition	Natural numbers greater than 1 that have no positive divisors other than 1 and themselves.	Natural numbers greater than 1 that have multiple positive divisors other than 1 and themselves.
Examples	2, 3, 5, 7, 11, 13, 17, 19, 23, . . .	4, 6, 8, 9, 10, 12, 14, 15, 21, . . .
Factors	Only have two distinct positive divisors, 1 and themselves.	Have more than two distinct positive divisors.
Divisibility	Cannot be divided evenly by any other natural number except 1 and itself.	Can be divided evenly by at least one natural number other than 1 and itself.
Number of Divisors	Prime numbers have exactly two divisors, 1 and the number itself.	Composite numbers have more than two divisors.
Density in the Set of Natural Numbers	Prime numbers are relatively sparse and become less frequent as numbers get larger.	Composite numbers are more common, especially as numbers get larger.
Examples	2, 3, 5, 7, 11, 13, 17, 19, 23, …	4, 6, 8, 9, 10, 12, 14, 15, 21, …

Applications of Composite Numbers

Composite numbers find applications in various fields due to their fundamental properties and relationships with prime numbers. Here are some applications of composite numbers:

1. Cryptography: Composite numbers play a crucial role in modern cryptography, particularly in public-key encryption algorithms like RSA (Rivest-Shamir-Adleman). In RSA encryption, the security of the system relies on the difficulty of factoring large composite numbers into their prime factors.
2. Factorization Algorithms: The study of composite numbers contributes to the development of factorization algorithms. These algorithms are essential for breaking down composite numbers into their prime factors efficiently. Factorization has applications in cryptography, number theory, and computer science.
3. Number Theory: Composite numbers serve as the basis for various concepts in number theory, including the study of divisors, factorization, and arithmetic functions. They provide valuable insights into the distribution and properties of natural numbers.
4. Divisibility Tests: Composite numbers are used in the development and testing of divisibility rules and algorithms. These rules help determine whether a number is divisible by another without performing actual division, making computations more efficient.
5. Mathematical Puzzles and Games: Composite numbers often feature in mathematical puzzles, games, and recreational mathematics. They serve as the basis for creating challenges, puzzles, and mathematical patterns that stimulate critical thinking and problem-solving skills.
6. Computer Science: Composite numbers are used in various computational tasks and algorithms. They feature in algorithms for generating prime numbers, testing primality, and factorization. In computer science, understanding the properties of composite numbers is essential for designing efficient algorithms and cryptographic systems.
7. Error Detection and Correction: In certain error detection and correction techniques, composite numbers are used as part of the encoding process. They help encode data in such a way that errors can be detected and corrected efficiently during transmission or storage.
8. Data Encryption and Security: Composite numbers are utilized in data encryption and security protocols beyond RSA. They form the basis of cryptographic systems that ensure the confidentiality, integrity, and authenticity of digital data in various applications, including secure communication and financial transactions.

Solved Questions on Composite Numbers

We have solve some questions on composite numbers down here:

Question 1: Determine the product of the first four composite numbers.

Solution:

The initial four composite numbers are 4, 6, 8, and 9.

As a result, the product of the first four composite numbers equals 4 x 6 x 8 x 9 = 1728

As a result, the sum of the first four composite numbers is 1728.

Question 2: Determine which of the following is not a composite number. 16, 36, 53, 78, 94.

Solution:

The correct answer is number 53. 53 is not a composite number because it can only be divided by one and itself.

Question 3: Determine whether 196 is a composite number.

Solution:

1, 2, 4, 7, 14, 28, 49, 98, and 196 are the factors of 196.

As a result, 196 is a composite number.

Question 4: What is 98’s prime factorization?

Solution:

98’s prime factorization is: 

98 = 2 × 7 × 7

Question 5: Determine if 183 and 196 are composite numbers.

Solution:

183 is not a composite number since it is not divisible by any other integer other than 1 and 183. Because 196 is divisible by two, it is a composite number.

Question 6: Which of the following is a composite number 13, 19, 22, 31?

Solution:

The correct answer is 22. Because a composite number is a positive integer larger than one with several divisors. In the example of 22, it may be divided evenly by 1, 2, 11, and 22, yielding a composite number.

Practice Problems on Composite Numbers

We have provided you with some practice problems on composite numbers to solve:

Q1: Identify whether the following numbers are composite or prime: 12, 17, 28, 31, 42, 47.

Q2: Find the prime factorization of the composite number 56.

Q3: List all the composite numbers between 30 and 50.

Q4: Determine if 99 is a composite number. If it is, find its prime factors.

Q5: Find the least common multiple (LCM) of 6 and 8.

FAQs on Composite Numbers

What is composite number?

A composite number in maths is a positive integer or a natural number with more than two factors. 16 is a composite number since it has components 1, 2, 4, 8, and 16.

What are the composite numbers less than 20?

Positive integers greater than one that have more than two divisors (1 and itself) are called composite numbers. Here is a list of composite numbers that are less than 20: 4, 6, 8, 9, 10, 12, 14, 15, 16, 18.

How many composite numbers exist between 1 and 50?

There are 34 composite numbers ranging from 1 to 50, as follows:

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.

Is 1 a composite number?

No, 1 is not a composite number. A composite number is defined as a positive integer greater than one that contains at least one positive divisor other than 1 and itself. In the case of 1, it has just one positive divisor, which is 1. As a result, 1 does not satisfy the concept of a composite number.

Is it true that all even numbers are composite?

No, all even integers are not composite numbers. Except for 2, all prime numbers are odd. However, all even integers, with the exception of 2, are composite numbers. Two is the prime number since it contains just two factors: 2 and 1.

Which numbers are neither prime nor composite?

The only number that is neither prime nor composite is 1. Because 1 has just one factor, and that element is 1 itself.

What is the smallest composite number you can think of?

The lowest composite number is 4. Furthermore, 1 is neither a prime nor a composite number, whereas 2 and 3 are primes.

What are the first five composite numbers?

The first five composite numbers are: 4, 6, 8 ,9, 10.

Are all composite numbers even?

No, not every composite number is even. While some composite numbers are even (such as 4, 6, 8, and so on), others are odd (such as 9, 15, 21, and so on).

How many composite numbers from 1 to 20?

There are ten composite numbers between 1 and 20: 4, 6, 8, 9, 10, 12, 14, 15, 16 and 18.

What are the composite numbers from 1 to 100?

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

What are examples of composite numbers?

Examples of composite numbers include:

• 4: Factors of 4 are 1, 2, and 4
• 6: Factors of 6 are 1, 2, 3, and 6
• 8: Factors of 8 are 1, 2, 4, and 8
• 9: Factors of 9 are 1, 3, and 9
• 10: Factors of 10 are 1, 2, 5, and 10
• 12: Factors of 12 are 1, 2, 3, 4, 6, and 12
• 14: Factors of 14 are 1, 2, 7, and 14
• 15: Factors of 15 are 1, 3, 5, and 15
• 16: Factors of 16 are 1, 2, 4, 8, and 16
• 18: Factors of 18 are 1, 2, 3, 6, 9, and 18