1. Types of Numbers
Numbers can be classified into different types based on their properties. Understanding these classifications is fundamental to all the maths you'll do in this course.
📌 Integers & Natural Numbers
Integer: A whole number that can be positive, negative, or zero.
Examples: -3, -2, -1, 0, 1, 2, 3
Natural Number: The positive integers (also called counting numbers). Zero is NOT included.
Examples: 1, 2, 3, 4, 5, ...
📌 Multiples & Factors
Multiple: A number formed by multiplying a given integer by another positive integer.
12 is a multiple of 3 because 12 = 3 × 4. Even numbers (2, 4, 6, ...) are multiples of 2.
Factor: A value that divides into a number exactly with no remainder.
6 is a factor of 18 because 18 ÷ 6 = 3
💡 Tip: To find all factors of a number, use factor pairs. For 18: (1,18), (2,9), (3,6). So factors are: 1, 2, 3, 6, 9, 18
📌 Divisibility Tests (No Calculator Needed!)
| Divisible by |
Test |
Example |
| 2 |
Last digit is 0, 2, 4, 6, or 8 |
134 ✓ (ends in 4) |
| 3 |
Sum of digits is divisible by 3 |
123 ✓ (1+2+3=6) |
| 5 |
Last digit is 0 or 5 |
3025 ✓ (ends in 5) |
| 10 |
Last digit is 0 |
2710 ✓ (ends in 0) |
📌 Prime Numbers
Prime Number: A number with exactly two distinct factors: itself and 1.
First 10 primes: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29
Remember: 1 is NOT prime (only 1 factor). 2 is the ONLY even prime.
📌 Square & Cube Numbers
Square Number: The result of multiplying a number by itself.
1² = 1, 2² = 4, 3² = 9, ... 15² = 225
Memorise the first 15: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225
Cube Number: The result of multiplying a number by itself twice.
1³ = 1, 2³ = 8, 3³ = 27, 4³ = 64, 5³ = 125
Memorise the first 5: 1, 8, 27, 64, 125. Also remember: 10³ = 1000
📌 Square & Cube Roots
Square Root: The number that when multiplied by itself equals the value. √49 = 7 because 7 × 7 = 49
⚠️ Important: √25 = 5, but -√25 = -5. Sometimes both ±√25 = ±5 are needed.
Surd: The square root of a non-perfect square. √3 is a surd because 3 is not a perfect square.
Surds are IRRATIONAL numbers (we'll cover this next).
Cube Root: The number that when multiplied by itself twice equals the value. ³√64 = 4 because 4 × 4 × 4 = 64
📌 Reciprocals
Reciprocal:
Q1: What are the factors of 24?
Q2: Explain why 51 is not a prime number.