Composite Numbers – Numbers with More Than Two Factors
A composite number is any whole number greater than 1 that is not prime — meaning it has at least one factor other than 1 and itself. In other words, it can be divided by some number in between.
Definition
A composite number has three or more factors (including 1 and itself). Equivalently, it can be written as a product of two smaller whole numbers.
Examples
| Number | Factors | Why Composite |
|---|---|---|
| 4 | 1, 2, 4 | Divisible by 2 |
| 12 | 1, 2, 3, 4, 6, 12 | Many factors |
| 15 | 1, 3, 5, 15 | Divisible by 3 and 5 |
| 100 | 1,2,4,5,10,20,25,50,100 | Many factors |
Composite Numbers from 1 to 30
4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28
Primes vs Composites vs 1
| Category | Definition | Examples |
|---|---|---|
| 1 | Neither prime nor composite | 1 only |
| Prime | Exactly 2 factors | 2, 3, 5, 7, 11... |
| Composite | 3 or more factors | 4, 6, 8, 9, 10... |
The Fundamental Theorem of Arithmetic
Every composite number can be expressed as a unique product of prime numbers. This is called the Fundamental Theorem of Arithmetic. For example, 60 = 2² × 3 × 5 — and no other prime factorization exists for 60.
Why Composites Matter
- They are the numbers we break apart in prime factorization.
- Identifying composites helps us find GCF and LCM.
- Many encryption schemes rely on the difficulty of factoring large composites.
Key Takeaways
- Composite = more than two factors.
- Every composite is divisible by at least one prime.
- Every composite has a unique prime factorization.
- 0 and 1 are neither prime nor composite.
Practice Questions
- Is 51 prime or composite? Show your reasoning.
- List all composite numbers between 30 and 40.
- What is the smallest composite number?
- True or false: all even numbers greater than 2 are composite.
- Find a composite number with exactly 4 factors.