What Are Factors?
A factor of a number is any whole number that divides into it exactly — with no remainder. Factors always come in pairs, and every number has at least two factors: 1 and itself.
The Key Test
A is a factor of B if B ÷ A leaves remainder 0.
Examples
Factors of 6
6 ÷ 1 = 6 ✓ 6 ÷ 2 = 3 ✓ 6 ÷ 3 = 2 ✓ 6 ÷ 4 = 1.5 ✗ 6 ÷ 5 = 1.2 ✗ 6 ÷ 6 = 1 ✓
Factors of 6: 1, 2, 3, 6
Factors of 20
Test 1 to 20: 20 ÷ 1 ✓ ÷2 ✓ ÷3 ✗ ÷4 ✓ ÷5 ✓ ÷6 ✗ ÷7 ✗ ÷8 ✗ ÷9 ✗ ÷10 ✓ ÷11–19 ✗ ÷20 ✓
Factors of 20: 1, 2, 4, 5, 10, 20
Important Properties
| Property | Example |
|---|---|
| 1 is a factor of every number | 1 ÷ 1 = 1, 7 ÷ 1 = 7 |
| Every number is a factor of itself | 15 ÷ 15 = 1 |
| Factors are always less than or equal to the number | Factors of 12 are all ≤ 12 |
| Factors come in pairs | 1×12, 2×6, 3×4 |
Factors vs Multiples
Students often confuse these two ideas. A simple way to remember: factors are smaller (they go into the number); multiples are larger (the number goes into them).
| Idea | Factors of 8 | Multiples of 8 |
|---|---|---|
| Direction | Divide INTO 8 | 8 multiplied by something |
| List | 1, 2, 4, 8 | 8, 16, 24, 32, 40... |
| Count | Finite (always ends) | Infinite (never ends) |
Key Takeaways
- A factor divides a number with remainder zero.
- Every number has 1 and itself as factors.
- Factors are finite; multiples are infinite.
- Knowing factors is essential for simplifying fractions and finding GCF.
Practice Questions
- List all factors of 15.
- Is 7 a factor of 49? Explain.
- How many factors does 1 have?
- List all factors of 36.
- True or false: 8 is a factor of 100.