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

1. List all factors of 20.
2. List all factors of 45.
3. Is 7 a factor of 56? Explain.
4. List the first 6 multiples of 9.
5. Is 72 a multiple of 8? Show why.
6. Is 15 prime or composite?
7. Is 29 prime or composite?
8. List all prime numbers between 20 and 40.

Level 2 – Developing

1. Find GCF(24, 36).
2. Find LCM(6, 8).
3. Find the prime factorization of 60.
4. Find GCF(42, 56) using prime factorization.
5. Find LCM(9, 12) using the GCF formula.
6. Draw a factor tree for 72.
7. Find all common factors of 18 and 30.
8. Simplify 36/48 using the GCF.

Level 3 – Advanced

1. Find LCM(12, 18, 30) using prime factorization.
2. Find GCF(126, 210) using the Euclidean algorithm.
3. Two numbers have GCF 8 and LCM 96. One is 24. Find the other.
4. Find the prime factorization of 5,040.
5. Add 5/12 + 7/18 using the LCM.
6. 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?
7. Find how many factors 360 has.
8. Find GCF(1,155, 2,310).

One More Question?