Factors, Multiples and Patterns: Class 5 Study Guide
Factors and multiples explain how numbers fit together, and they help with fractions.
A factor of a number divides it exactly. The factors of 12 are 1, 2, 3, 4, 6 and 12. A multiple of a number is found by multiplying it by 1, 2, 3 and so on. The multiples of 4 are 4, 8, 12, 16, 20…
A prime number has exactly two factors, 1 and itself (2, 3, 5, 7, 11…). A composite number has more than two factors (4, 6, 8, 9, 10…). The number 1 is neither prime nor composite.
Divisibility tests
| Divisible by | Test | Example |
|---|---|---|
| 2 | last digit is 0, 2, 4, 6 or 8 | 358 yes |
| 3 | digit sum divisible by 3 | 123: 1+2+3 = 6 yes |
| 5 | last digit is 0 or 5 | 745 yes |
| 9 | digit sum divisible by 9 | 729: 18 yes |
| 10 | last digit is 0 | 380 yes |
HCF and LCM
The highest common factor (HCF) is the largest number that divides both numbers. For 12 and 18, the factors of 12 are 1, 2, 3, 4, 6, 12 and the factors of 18 are 1, 2, 3, 6, 9, 18, so the HCF is 6. The lowest common multiple (LCM) is the smallest number that is a multiple of both. The multiples of 4 are 4, 8, 12, 16 and of 6 are 6, 12, 18, so the LCM is 12.
Write them in order.
Those in both lists.
HCF is the largest common factor.
Does it divide both numbers?
Using them in problems
HCF answers sharing questions: 12 pencils and 18 erasers are packed into identical sets with nothing left over. The most sets is 6 (HCF), each with 2 pencils and 3 erasers. LCM answers 'when will they meet again' problems: two lights flash every 4 and 6 seconds, so they flash together every 12 seconds. LCM also gives a common denominator for adding fractions.
Worked examples and common mistakes
Example: Is 91 prime? 91 = 7 × 13, so it is composite. Common mistakes: calling 1 a prime number, mixing up factors (small) with multiples (large) and stopping at the first common factor instead of finding the highest. Use factor pairs to be sure you have found them all.
Check your understanding: model answers
1. 1, 2, 4, 5, 10, 20. 2. 15. 3. Yes, 5 + 7 = 12, which is divisible by 3 (57 = 3 × 19).
✨ Key Takeaways
- Factors divide a number; multiples are its times table.
- A prime number has exactly two factors.
- HCF is for sharing; LCM is for repeating events.
- 1 is neither prime nor composite.
💬 Questions for Discussion & Reflection
- List the factors of 20.
- Find the LCM of 3 and 5.
- Is 57 divisible by 3?