Playing with Numbers: Factors, Multiples, HCF and LCM: Class 6 Study Guide
Factors, multiples and primes help us split, share and compare numbers.
A factor divides a number exactly. The factors of 12 are 1, 2, 3, 4, 6 and 12. A multiple is a number in its times table, so the multiples of 4 are 4, 8, 12, 16 and so on. A prime number has exactly two factors, 1 and itself (2, 3, 5, 7, 11). A composite number has more than two factors. The number 1 is neither prime nor composite.
Every composite number can be written as a product of primes, called prime factorisation. For example 60 = 2 × 2 × 3 × 5.
Divisibility rules
| Divisor | Rule |
|---|---|
| 2 | Last digit is 0, 2, 4, 6 or 8 |
| 3 | Sum of digits is divisible by 3 |
| 4 | Last two digits are divisible by 4 |
| 5 | Last digit is 0 or 5 |
| 6 | Divisible by both 2 and 3 |
| 9 | Sum of digits is divisible by 9 |
| 10 | Last digit is 0 |
HCF and LCM
The HCF (highest common factor) is the largest number that divides both numbers. The LCM (lowest common multiple) is the smallest number that both divide into. For 12 and 18, the factors are 12: 1, 2, 3, 4, 6, 12 and 18: 1, 2, 3, 6, 9, 18, so HCF = 6. The multiples of 12 are 12, 24, 36 and of 18 are 18, 36, so LCM = 36. Check: HCF × LCM = 6 × 36 = 216 = 12 × 18.
Of each number.
Take common primes, lowest powers.
Take all primes, highest powers.
HCF × LCM = product of the two.
Word problems
Use HCF to share things into the biggest equal groups: 12 pens and 18 pencils can be put in 6 equal packets. Use LCM for events that repeat: if one bell rings every 12 minutes and another every 18, they ring together every 36 minutes.
Worked examples and common mistakes
Example: Is 135 divisible by 3? 1 + 3 + 5 = 9, so yes. Example: Prime factors of 36: 2 × 2 × 3 × 3. Common mistakes: calling 1 a prime, calling 2 not prime (it is the only even prime), and mixing up HCF and LCM.
Check your understanding: model answers
1. HCF 4 and LCM 24. 2. No, 91 = 7 × 13. 3. 4 + 7 + 2 + 5 = 18, so yes.
✨ Key Takeaways
- A prime has exactly two factors.
- Divisibility rules save time.
- HCF is the greatest common factor and LCM the least common multiple.
- HCF × LCM = product of the two numbers.
💬 Questions for Discussion & Reflection
- Find the HCF and LCM of 8 and 12.
- Is 91 prime?
- Is 4,725 divisible by 9?
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