Year 8 Prime Factorisation (Factor Trees) Worksheet — Level 3 — 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 3 — Practice Set 3 — Answers
Keep splitting each number into two factors until every branch ends in a prime. Write repeated factors with an index, e.g. 2 × 2 × 2 = 23.
1.Use a factor tree to write 165 as a product of prime factors in index form.
Answer: 3×5×11
- 165 = 3 × 55
- 55 = 5 × 11
- So 165 = 3 × 5 × 11 = 3 × 5 × 11
2.Which number has the prime factorisation 32 × 7?
Answer: 63
- 3 × 3 × 7 = 63
3.Use a factor tree to write 500 as a product of prime factors in index form.
Answer: 22×53
- 500 = 2 × 250
- 250 = 2 × 125
- 125 = 5 × 25
- 25 = 5 × 5
- So 500 = 2 × 2 × 5 × 5 × 5 = 22 × 53
4.Which number has the prime factorisation 52 × 11?
Answer: 275
- 5 × 5 × 11 = 275
5.Use a factor tree to write 210 as a product of prime factors in index form.
Answer: 2×3×5×7
- 210 = 2 × 105
- 105 = 3 × 35
- 35 = 5 × 7
- So 210 = 2 × 3 × 5 × 7 = 2 × 3 × 5 × 7
6.Which number has the prime factorisation 2 × 3 × 11?
Answer: 66
- 2 × 3 × 11 = 66
7.Use a factor tree to write 105 as a product of prime factors in index form.
Answer: 3×5×7
- 105 = 3 × 35
- 35 = 5 × 7
- So 105 = 3 × 5 × 7 = 3 × 5 × 7
8.Which number has the prime factorisation 3 × 5 × 7?
Answer: 105
- 3 × 5 × 7 = 105
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.