1. Introduction to Composite Numbers
Composite numbers are the opposite of prime numbers. While prime numbers have only two factors, composite numbers have more than two factors.
Understanding composite numbers helps you with factors, multiples, prime factorization, and many arithmetic concepts.
2. Definition of Composite Numbers
A composite number is a whole number greater than 1 that has more than two factors.
In simple words: If a number can be divided evenly by other numbers besides 1 and itself, it is composite.
Examples:
- 4 → factors: 1, 2, 4 → composite
- 6 → factors: 1, 2, 3, 6 → composite
- 9 → factors: 1, 3, 9 → composite
3. Why 1 Is NOT a Composite Number
A composite number must have more than two factors. But 1 has only one factor: 1.
So, 1 is neither prime nor composite.
4. Smallest Composite Number
The smallest composite number is 4.
Because:
- 4 > 1
- 4 has more than two factors: 1, 2, and 4
5. How to Identify Composite Numbers
There are simple ways to check if a number is composite.
5.1. Check Number of Factors
If a number has 3 or more factors, it is composite.
Example: 10
- Factors: 1, 2, 5, 10
Since it has 4 factors, 10 is composite.
5.2. Divisibility Test
Check if the number is divisible by smaller numbers.
Example: Is 15 composite?
- 15 ÷ 3 = 5 → exact
Since 15 is divisible by 3, it is composite.
5.3. Use Prime Factorization
If a number can be broken into prime factors, it is composite.
Example: 20
20 = 2 × 2 × 5 → composite
6. Examples of Composite Numbers
Here are some composite numbers:
4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25...
7. Prime Factorization of Composite Numbers
Every composite number can be expressed as a product of prime numbers. This is called prime factorization.
7.1. Examples
- 12 = 2 × 2 × 3
- 18 = 2 × 3 × 3
- 45 = 3 × 3 × 5
7.2. Using Factor Trees
Factor trees help break a composite number into prime factors step by step.
8. Properties of Composite Numbers
Composite numbers follow a few simple rules:
8.1. Always Have More Than Two Factors
This is the key property. If a number has only two factors, it is prime—not composite.
8.2. All Even Numbers Except 2 Are Composite
Because any even number ≥ 4 can be divided by 2.
Examples: 4, 6, 8, 10...
8.3. Composite Numbers Can Be Written as Products
Every composite number can be expressed as the multiplication of two or more smaller numbers.
Example: 15 = 3 × 5
9. Composite Numbers in Real Life
Composite numbers appear wherever grouping, arranging, and factor-based calculations are needed.
9.1. Tiling and Patterns
Numbers like 12, 16, and 20 help in arranging objects evenly in rows and columns.
9.2. Fractions and Ratios
Composite numbers break easily into smaller parts, making them useful in measurement and scaling.
9.3. Coding and Algorithms
Composite numbers are used in factor-based algorithms and optimization problems.
10. Difference Between Prime and Composite Numbers
Prime and composite numbers are opposite in terms of factors.
10.1. Comparison Table
| Prime Numbers | Composite Numbers |
|---|---|
| Exactly 2 factors | More than 2 factors |
| Examples: 2, 3, 5, 7 | Examples: 4, 6, 8, 9, 10 |
| Cannot be broken into smaller factors | Can be broken into prime factors |