Year 8 Prime Factorisation (Factor Trees) Worksheet — Level 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 — 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 72 × 11?
Answer: 539
- 7 × 7 × 11 = 539
3.Use a factor tree to write 450 as a product of prime factors in index form.
Answer: 2×32×52
- 450 = 2 × 225
- 225 = 3 × 75
- 75 = 3 × 25
- 25 = 5 × 5
- So 450 = 2 × 3 × 3 × 5 × 5 = 2 × 32 × 52
4.Which number has the prime factorisation 22 × 7 × 11?
Answer: 308
- 2 × 2 × 7 × 11 = 308
5.Use a factor tree to write 462 as a product of prime factors in index form.
Answer: 2×3×7×11
- 462 = 2 × 231
- 231 = 3 × 77
- 77 = 7 × 11
- So 462 = 2 × 3 × 7 × 11 = 2 × 3 × 7 × 11
6.Which number has the prime factorisation 52 × 7?
Answer: 175
- 5 × 5 × 7 = 175
7.Use a factor tree to write 100 as a product of prime factors in index form.
Answer: 22×52
- 100 = 2 × 50
- 50 = 2 × 25
- 25 = 5 × 5
- So 100 = 2 × 2 × 5 × 5 = 22 × 52
8.Which number has the prime factorisation 3 × 52?
Answer: 75
- 3 × 5 × 5 = 75
Marking tips
- Give credit for correct method even when the final answer slips — the working shows where the thinking went right.
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