Number Properties
Primes, factors, multiples, HCF, LCM and divisibility rules
Explanation
Types of Numbers
| Type | Definition | Examples |
|---|---|---|
| Even numbers | Divisible by 2 | 2, 4, 6, 8, 10 ... |
| Odd numbers | Not divisible by 2 | 1, 3, 5, 7, 9 ... |
| Prime numbers | Exactly 2 factors (1 and itself) | 2, 3, 5, 7, 11, 13 ... |
| Composite numbers | More than 2 factors | 4, 6, 8, 9, 10 ... |
| Square numbers | n² | 1, 4, 9, 16, 25, 36 ... |
| Cube numbers | n³ | 1, 8, 27, 64, 125 ... |
Important: 1 is neither prime nor composite. 2 is the only even prime.
Factors, Multiples, HCF & LCM
- Factors of 12: 1, 2, 3, 4, 6, 12 (divide evenly into 12)
- Multiples of 4: 4, 8, 12, 16, 20 ... (the 4 times table)
HCF (Highest Common Factor): largest number dividing into both.
HCF of 18 and 24: factors of 18 = {1,2,3,6,9,18}, factors of 24 = {1,2,3,4,6,8,12,24} → HCF = 6
LCM (Lowest Common Multiple): smallest number that is a multiple of both.
LCM of 4 and 6: multiples of 4 = 4, 8, 12 ... multiples of 6 = 6, 12 ... → LCM = 12
Divisibility Rules
| Divisible by | Rule |
|---|---|
| 2 | Last digit is even (0, 2, 4, 6, 8) |
| 3 | Sum of digits is divisible by 3 |
| 4 | Last two digits divisible by 4 |
| 5 | Last digit is 0 or 5 |
| 9 | Sum of digits is divisible by 9 |
| 10 | Last digit is 0 |
Key Tips
- Memorise primes up to 50: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47
- HCF is used for simplifying fractions; LCM is used for adding/subtracting fractions
- Shortcut: HCF × LCM = product of the two numbers
Sample Practice Questions
-
What is the HCF of 24 and 36?
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Answer: 12
-
What is the HCF of 8 and 12?
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Answer: 4
-
What is the LCM of 6 and 9?
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Answer: 18
-
What is the LCM of 4 and 6?
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Answer: 12
Practice Questions
Test your knowledge of Number Properties with a timed quiz. Answers are revealed at the end.
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What does Number Properties cover in the Selective Entry Numerical Reasoning exam?
Primes, factors, multiples, HCF, LCM and divisibility rules.
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