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Prime Factorisation Practice Worksheet
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Prime Factorisation Practice Worksheet
📚 Part 1: Understanding Prime Factorisation
1. Which of the following numbers is a prime number?
15
17
21
25
2. What is the prime factorisation of 12?
2 × 6
3 × 4
2² × 3
2 × 3 × 4
3. Which of these are prime factors of 30? (Select all that apply)
2
3
5
6
10
4. The prime factorisation of 36 is:
2² × 3²
6²
2 × 3 × 6
4 × 9
✏️ Part 2: Finding Prime Factors
5. Find the prime factorisation of 24. Show your working using a factor tree.
6. Write the prime factorisation of 60 in index form (using powers).
7. Find the prime factorisation of 84. Show your working.
8. Complete: 72 = 2³ × ____
72 = 2³ × ________
🧩 Part 3: Problem Solving
9. Sarah is arranging 48 books into equal rows. She wants to use only prime numbers for the number of books per row. List all the possible arrangements she could make.
10. Two numbers have the prime factorisation 2² × 3 and 2 × 3² respectively. What is the prime factorisation of their product?
11. A rectangular garden has an area of 42 square metres. If both the length and width must be prime numbers, what are the possible dimensions?
12. Challenge: Find a number between 50 and 60 that has exactly three different prime factors. Show the prime factorisation.
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