Year 7 Prime Factorisation (Factor Trees) Worksheet — Level 2 — Practice Set 3 — Answers
Answer sheet with worked solutions for the Year 7 factors, multiples & primes worksheet.
Success TutoringWorksheetsAnswer sheetYear 7 · Mathematics · Factors, Multiples & PrimesYear 7 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 100 as a product of prime factors.
Answer: 2×2×5×5
- 100 = 2 × 50
- 50 = 2 × 25
- 25 = 5 × 5
- So 100 = 2 × 2 × 5 × 5 = 22 × 52
2.Use a factor tree to write 135 as a product of prime factors.
Answer: 3×3×3×5
- 135 = 3 × 45
- 45 = 3 × 15
- 15 = 3 × 5
- So 135 = 3 × 3 × 3 × 5 = 33 × 5
3.Use a factor tree to write 162 as a product of prime factors.
Answer: 2×3×3×3×3
- 162 = 2 × 81
- 81 = 3 × 27
- 27 = 3 × 9
- 9 = 3 × 3
- So 162 = 2 × 3 × 3 × 3 × 3 = 2 × 34
4.Which number has the prime factorisation 32 × 7?
Answer: 63
- 3 × 3 × 7 = 63
5.Use a factor tree to write 126 as a product of prime factors.
Answer: 2×3×3×7
- 126 = 2 × 63
- 63 = 3 × 21
- 21 = 3 × 7
- So 126 = 2 × 3 × 3 × 7 = 2 × 32 × 7
6.Use a factor tree to write 210 as a product of prime factors.
Answer: 2×3×5×7
- 210 = 2 × 105
- 105 = 3 × 35
- 35 = 5 × 7
- So 210 = 2 × 3 × 5 × 7
7.Use a factor tree to write 175 as a product of prime factors.
Answer: 5×5×7
- 175 = 5 × 35
- 35 = 5 × 7
- So 175 = 5 × 5 × 7 = 52 × 7
8.Which number has the prime factorisation 2 × 32 × 5?
Answer: 90
- 2 × 3 × 3 × 5 = 90
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.