Factors, Multiples, Primes and Order of Operations: Year 6 Study Guide
Understanding how numbers are built makes fractions, algebra and problem solving easier.
A factor divides a number exactly: the factors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24. A multiple is found by multiplying: multiples of 6 are 6, 12, 18, 24… A prime number has exactly two factors (itself and 1): 2, 3, 5, 7, 11. A composite number has more than two. The number 1 is neither.
A square number is the result of multiplying a number by itself (4² = 16), and a cube number comes from multiplying three equal factors (3³ = 27). Year 6 students also use the order of operations: brackets, then multiplication and division, then addition and subtraction.
Divisibility rules
| Divisible by | Rule | Example |
|---|---|---|
| 2 | ends in 0, 2, 4, 6, 8 | 348 |
| 3 | digits add to a multiple of 3 | 174 (1+7+4 = 12) |
| 4 | last two digits divisible by 4 | 316 |
| 5 | ends in 0 or 5 | 645 |
| 9 | digits add to a multiple of 9 | 729 |
| 10 | ends in 0 | 480 |
HCF and LCM
The highest common factor (HCF) of 12 and 20 is 4. The lowest common multiple (LCM) of 4 and 6 is 12. Use the HCF to simplify fractions (12/20 = 3/5) and the LCM to find a common denominator or when events repeat together. A prime factor tree shows a number as a product of primes: 60 = 2 × 2 × 3 × 5.
In order.
In both lists.
HCF or LCM.
Does it divide both?
Order of operations
Brackets first, then multiplication and division from left to right, then addition and subtraction from left to right. 5 + 3 × 4 = 17, but (5 + 3) × 4 = 32. 20 − 12 ÷ 3 = 16. Calculators with scientific functions follow the same order; basic ones may not, so check.
Worked examples and common mistakes
Example: Is 91 prime? 7 × 13 = 91, so no. Common mistakes: calling 1 prime, mixing up HCF and LCM and working left to right without respecting multiplication. Estimate to check that an answer is reasonable.
Check your understanding: model answers
1. 1, 2, 3, 6, 9, 18. 2. 24. 3. 3 + 4 × 4 = 19.
✨ Key Takeaways
- Factors divide; multiples are times tables.
- Primes have exactly two factors.
- HCF simplifies; LCM finds common denominators.
- Brackets, × ÷, then + −.
💬 Questions for Discussion & Reflection
- List the factors of 18.
- Find the LCM of 6 and 8.
- Work out 3 + 4 × (6 − 2).