Types of Numbers
- Natural Numbers (N): 1, 2, 3, 4, … (counting numbers)
- Whole Numbers (W): 0, 1, 2, 3, … (natural numbers + 0)
- Integers (Z): …−3, −2, −1, 0, 1, 2, 3… (positive + negative + 0)
- Rational Numbers: Can be expressed as p/q where q ≠ 0 (fractions, terminating/repeating decimals)
- Irrational Numbers: Cannot be expressed as p/q — √2, √3, π, e
- Real Numbers: Rational + Irrational
Prime & Composite Numbers
- Prime numbers: Exactly 2 factors (1 and itself) — 2, 3, 5, 7, 11, 13, 17, 19, 23, 29…
- 2 is the only even prime number
- Composite numbers: More than 2 factors — 4, 6, 8, 9…
- 1 is neither prime nor composite
- Total prime numbers between 1-100: 25
Divisibility Rules
| Divisor | Rule |
|---|
| 2 | Last digit is 0, 2, 4, 6 or 8 (even) |
| 3 | Sum of digits divisible by 3 |
| 4 | Last two digits divisible by 4 |
| 5 | Last digit is 0 or 5 |
| 6 | Divisible by both 2 and 3 |
| 8 | Last three digits divisible by 8 |
| 9 | Sum of digits divisible by 9 |
| 10 | Last digit is 0 |
| 11 | (Sum of odd-position digits) − (Sum of even-position digits) = 0 or multiple of 11 |
Face Value & Place Value
- Face Value: The digit itself, regardless of position (face value of 7 in 4753 is 7)
- Place Value: Digit × value of its position (place value of 7 in 4753 is 700)
💡 A number is divisible by a composite number (like 6, 12, 15) if it's divisible by all of that number's prime factors.