What is a Composite Number? Definition, Table & Key Properties
The concept of composite numbers is fundamental in mathematics. Understanding what makes a number composite is crucial for topics like factors, divisibility, and prime factorization. This topic regularly appears in school exams and is also useful in real-life number reasoning.
What Is a Composite Number?
A composite number is a positive integer greater than 1 that has more than two factors. Simply put, a composite number can be divided exactly by numbers other than 1 and itself. In contrast, prime numbers only have two factors. For example, 6 is composite because it is divisible by 1, 2, 3, and 6.
How to Identify Composite Numbers
To identify if a number is composite, follow these quick steps:
- Write all factors of the number.
- If you find more than two factors (1 and itself plus at least one more), it’s a composite number.
- If the number has only two factors (1 and itself), it is not composite—it’s prime.
For example, 9 has factors 1, 3, and 9 (so it is composite); 7 has only 1 and 7 (so it is prime).
Composite Numbers List from 1 to 100
Here’s an easy-to-read table showing all composite numbers between 1 and 100 for quick revision:
| Number | Composite? | Factors (other than 1 & itself) |
|---|---|---|
| 4 | Yes | 2 |
| 6 | Yes | 2, 3 |
| 8 | Yes | 2, 4 |
| 9 | Yes | 3 |
| 10 | Yes | 2, 5 |
| 12 | Yes | 2, 3, 4, 6 |
| 14 | Yes | 2, 7 |
| 15 | Yes | 3, 5 |
| 16 | Yes | 2, 4, 8 |
| 18 | Yes | 2, 3, 6, 9 |
| 20 | Yes | 2, 4, 5, 10 |
| ... | ... | ... |
| 100 | Yes | 2, 4, 5, 10, 20, 25, 50 |
Some more examples: 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, up to 100. The smallest composite number is 4.
Properties of Composite Numbers
- Every composite number is a positive integer greater than 1 with more than two factors.
- All even numbers greater than 2 are composite (since they are divisible by 2).
- Any composite number can be written as a product of two or more prime numbers.
- There are both even and odd composite numbers (e.g., 4 is even composite, 9 is odd composite).
- 1 is not composite; it has only one factor (itself).
Types of Composite Numbers
Even Composite Numbers: Composite numbers that are also even (e.g., 4, 6, 8, 10).
Odd Composite Numbers: Composite numbers that are odd (e.g., 9, 15, 21).
Prime vs Composite Numbers – What’s the Difference?
| Prime Number | Composite Number |
|---|---|
| Has only 2 factors (1 & itself) | Has more than 2 factors |
| Examples: 2, 3, 5, 7, 11 | Examples: 4, 6, 8, 9, 10 |
| Cannot be written as a product of smaller numbers (except 1 × itself) | Can be expressed as a product of prime numbers |
| Smallest prime is 2 | Smallest composite is 4 |
Learn more about prime numbers for deeper understanding.
Examples and Step-by-Step Solutions
Q: Is 14 a composite number?
1. List the factors: 1, 2, 7, 14
2. More than two factors? Yes (2 and 7).
3. So, 14 is a composite number.
Q: Is 2 a composite number?
1. Factors: 1, 2
2. Only two factors.
3. Thus, 2 is not composite (it is prime).
Practice: Try These Yourself
- Write the first five composite numbers.
- Check if 48 is a composite number (find its factors).
- List all composite numbers between 30 and 50.
- Is 93 composite or prime?
Frequent Errors and Misunderstandings
- Thinking that 1 is composite (it’s neither prime nor composite).
- Assuming all even numbers are composite (2 is even but prime).
- Missing “hidden” factors when counting divisors.
- Forgetting that prime factorization is only for composite numbers.
Relation to Other Concepts
Understanding composite numbers is closely linked to topics like factors and multiples, prime factorization, and natural numbers. Mastery here helps with LCM, HCF, and solving fractional problems in algebra.
Classroom Tip
A quick trick—if a number is not prime and is not 1, it is composite. Divisibility tests help spot composites. Vedantu teachers often use color-coded factor trees or tables to make this clear in classes.
We explored composite numbers—their definition, properties, differences, examples, and links to other maths ideas. For more in-depth explanations and live examples, check out free Vedantu classes or connect with expert teachers any time. Keep practicing to boost confidence with numbers!
Related learning: Prime Numbers | Factors and Multiples | Prime Factorization | Types of Numbers
FAQs on Composite Numbers – Definition, List & Examples
1. What is a composite number?
A composite number is a positive integer greater than 1 that has more than two factors. This means it can be divided evenly by numbers other than 1 and itself. For example, 4 is a composite number because its factors are 1, 2, and 4.
2. Is 2 a composite number?
No, 2 is not a composite number. It is a prime number because it only has two factors: 1 and itself. Composite numbers must have more than two factors.
3. What are the first 20 composite numbers?
The first twenty composite numbers are: 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32.
4. How do you know if a number is composite?
To determine if a number is composite, find its factors. If it has more than two factors (excluding 1 and itself), it's a composite number. You can use methods like divisibility rules to help identify factors efficiently.
5. What is the difference between prime and composite numbers?
A prime number is a whole number greater than 1 that has only two factors: 1 and itself. A composite number is a whole number greater than 1 that has more than two factors. The number 1 is neither prime nor composite.
6. Is 93 a prime or composite number?
93 is a composite number. It is divisible by 3 and 31, in addition to 1 and itself.
7. What is the smallest composite number?
The smallest composite number is 4. Its factors are 1, 2, and 4.
8. Can composite numbers be odd?
Yes, composite numbers can be odd. For example, 9 (factors: 1, 3, 9) and 15 (factors: 1, 3, 5, 15) are odd composite numbers.
9. Are all even numbers composite?
No, not all even numbers are composite. The number 2 is an even number, but it is a prime number because it only has two factors: 1 and 2.
10. How are composite numbers used in factorization?
Composite numbers are fundamental in factorization. They can be broken down into smaller factors, ultimately leading to their prime factorization (expressing the number as a product of only prime numbers). This is crucial for simplifying expressions and solving various mathematical problems.
11. What are consecutive composite numbers?
Consecutive composite numbers are a sequence of composite numbers that follow one another without any prime numbers in between. For example, 24, 25, 26, 27, 28 are consecutive composite numbers.
12. List the composite numbers between 1 and 10.
The composite numbers between 1 and 10 are 4, 6, 8, 9, and 10.
