Year 8 Prime Factorisation (Factor Trees) Worksheet — Level 2 — Practice Set 3 — Answers
Answer sheet with worked solutions for the Year 8 factors, multiples & primes worksheet.
Success TutoringWorksheetsAnswer sheetYear 8 · Mathematics · Factors, Multiples & PrimesYear 8 Prime Factorisation (Factor Trees) Worksheet — Level 2 — Practice Set 3 — Answers
Keep splitting each number into two factors until every branch ends in a prime. Write the primes from smallest to largest.
1.Use a factor tree to write 105 as a product of prime factors.
Answer: 3×5×7
- 105 = 3 × 35
- 35 = 5 × 7
- So 105 = 3 × 5 × 7
2.Use a factor tree to write 48 as a product of prime factors.
Answer: 2×2×2×2×3
- 48 = 2 × 24
- 24 = 2 × 12
- 12 = 2 × 6
- 6 = 2 × 3
- So 48 = 2 × 2 × 2 × 2 × 3 = 24 × 3
3.Use a factor tree to write 42 as a product of prime factors.
Answer: 2×3×7
- 42 = 2 × 21
- 21 = 3 × 7
- So 42 = 2 × 3 × 7
4.Which number has the prime factorisation 2 × 3 × 72?
Answer: 294
- 2 × 3 × 7 × 7 = 294
5.Use a factor tree to write 75 as a product of prime factors.
Answer: 3×5×5
- 75 = 3 × 25
- 25 = 5 × 5
- So 75 = 3 × 5 × 5 = 3 × 52
6.Use a factor tree to write 140 as a product of prime factors.
Answer: 2×2×5×7
- 140 = 2 × 70
- 70 = 2 × 35
- 35 = 5 × 7
- So 140 = 2 × 2 × 5 × 7 = 22 × 5 × 7
7.Use a factor tree to write 63 as a product of prime factors.
Answer: 3×3×7
- 63 = 3 × 21
- 21 = 3 × 7
- So 63 = 3 × 3 × 7 = 32 × 7
8.Which number has the prime factorisation 2 × 34?
Answer: 162
- 2 × 3 × 3 × 3 × 3 = 162
Marking tips
- Give credit for correct method even when the final answer slips — the working shows where the thinking went right.
- For open-ended tasks, use the success criteria as a checklist rather than looking for one "right" answer.
- Celebrate what went well first, then pick one thing to work on next.