Prime and Composite Numbers
Welcome to the fascinating world of prime and composite numbers! These special numbers are the building blocks of all mathematics.
1. What is a Divisor?
Definition: A divisor is a number that divides another number exactly (without any remainder).
Example: Divisors of 12
- 12 ÷ 1 = 12 ✓ (no remainder)
- 12 ÷ 2 = 6 ✓ (no remainder)
- 12 ÷ 3 = 4 ✓ (no remainder)
- 12 ÷ 4 = 3 ✓ (no remainder)
- 12 ÷ 6 = 2 ✓ (no remainder)
- 12 ÷ 12 = 1 ✓ (no remainder)
Divisors of 12: 1, 2, 3, 4, 6, 12
Key Fact: Every number has at least TWO divisors:
- 1 (because any number ÷ 1 = itself)
- The number itself (because any number ÷ itself = 1)
Interactive visualization — available in the full lesson
2. Finding All Divisors
Method: Check each number from 1 to n
To find all divisors of 18:
| Division | Result | Divisor? |
|---|---|---|
| 18 ÷ 1 | 18 | Yes ✓ |
| 18 ÷ 2 | 9 | Yes ✓ |
| 18 ÷ 3 | 6 | Yes ✓ |
| 18 ÷ 4 | 4.5 | No ✗ |
| 18 ÷ 5 | 3.6 | No ✗ |
| 18 ÷ 6 | 3 | Yes ✓ |
| 18 ÷ 9 | 2 | Yes ✓ |
| 18 ÷ 18 | 1 | Yes ✓ |
Divisors of 18: 1, 2, 3, 6, 9, 18 (6 divisors)
Shortcut: Divisor Pairs!
Divisors come in pairs that multiply to give the number:
- 1 × 18 = 18
- 2 × 9 = 18
- 3 × 6 = 18
So you only need to check up to the square root!
Interactive visualization — available in the full lesson