Year 7 Prime Factorisation (Factor Trees) Worksheet — Level 3 — Practice Set 2 — 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 3 — Practice Set 2 — 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 180 as a product of prime factors in index form.
Answer: 22×32×5
- 180 = 2 × 90
- 90 = 2 × 45
- 45 = 3 × 15
- 15 = 3 × 5
- So 180 = 2 × 2 × 3 × 3 × 5 = 22 × 32 × 5
2.Which number has the prime factorisation 3 × 5 × 72?
Answer: 735
- 3 × 5 × 7 × 7 = 735
3.Use a factor tree to write 693 as a product of prime factors in index form.
Answer: 32×7×11
- 693 = 3 × 231
- 231 = 3 × 77
- 77 = 7 × 11
- So 693 = 3 × 3 × 7 × 11 = 32 × 7 × 11
4.Which number has the prime factorisation 2 × 5 × 72?
Answer: 490
- 2 × 5 × 7 × 7 = 490
5.Use a factor tree to write 126 as a product of prime factors in index form.
Answer: 2×32×7
- 126 = 2 × 63
- 63 = 3 × 21
- 21 = 3 × 7
- So 126 = 2 × 3 × 3 × 7 = 2 × 32 × 7
6.Which number has the prime factorisation 3 × 52?
Answer: 75
- 3 × 5 × 5 = 75
7.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
8.Which number has the prime factorisation 3 × 112?
Answer: 363
- 3 × 11 × 11 = 363
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.