Factors, Multiples & Primes
Factors and Multiples – Practice Exercises
Work through these exercises to consolidate your understanding. Answers are provided at the end of each section.
For the best results, attempt every question in a level before checking the answer box beneath it — resist the temptation to peek early. If you get a question wrong, don’t just note the correct answer; go back to the relevant topic page in this section and work through the reasoning again until the method itself makes sense, not just this particular number.
Level 1 – Foundations
- List all factors of 20.
- List all factors of 45.
- Is 7 a factor of 56? Explain.
- List the first 6 multiples of 9.
- Is 72 a multiple of 8? Show why.
- Is 15 prime or composite?
- Is 29 prime or composite?
- List all prime numbers between 20 and 40.
Answers (Level 1): 1. {1,2,4,5,10,20}. 2. {1,3,5,9,15,45}. 3. Yes, 56÷7=8. 4. 9,18,27,36,45,54. 5. Yes, 72÷8=9. 6. Composite. 7. Prime. 8. 23,29,31,37.
Level 2 – Developing
- Find GCF(24, 36).
- Find LCM(6, 8).
- Find the prime factorization of 60.
- Find GCF(42, 56) using prime factorization.
- Find LCM(9, 12) using the GCF formula.
- Draw a factor tree for 72.
- Find all common factors of 18 and 30.
- Simplify 36/48 using the GCF.
Answers (Level 2): 1. 12. 2. 24. 3. 2²×3×5. 4. GCF=14. 5. GCF(9,12)=3; LCM=36. 6. 72=2³×3². 7. {1,2,3,6}. 8. 3/4.
Level 3 – Advanced
- Find LCM(12, 18, 30) using prime factorization.
- Find GCF(126, 210) using the Euclidean algorithm.
- Two numbers have GCF 8 and LCM 96. One is 24. Find the other.
- Find the prime factorization of 5,040.
- Add 5/12 + 7/18 using the LCM.
- A school library shelves 84 fiction books and 120 non-fiction books in equal-sized stacks with no books left over. What is the maximum stack size?
- Find how many factors 360 has.
- Find GCF(1,155, 2,310).
Answers (Level 3): 1. 180. 2. GCF=42. 3. 32. 4. 2⁴×3²×5×7. 5. 29/36. 6. 12 books. 7. 360=2³×3²×5 → (3+1)(2+1)(1+1)=24 factors. 8. GCF=1,155.
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