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Edexcel 1MA1 GCSE Maths · 3 Worked Solutions

Edexcel GCSE Maths: Number Worked Solutions

Real mark-scheme-derived worked solutions for Edexcel GCSE Maths Number questions. Every solution includes step-by-step working, the correct final answer, marks awarded, and a common mistake callout — with question-level AO breakdown from the official 1MA1 spec.

Q1 Foundation 2 marks
Edexcel 1MA1 · 2024

Question

Find the highest common factor (HCF) of 63 and 105

Worked Solution

  1. Find the prime factors of 63: 63 = 3 × 21 = 3 × 3 × 7 = 3² × 7.

  2. Find the prime factors of 105: 105 = 3 × 35 = 3 × 5 × 7.

  3. Identify the prime factors common to both: both have 3 (appearing once in 105) and 7.

  4. HCF = 3 × 7 = 21.

Final Answer

21

Common Mistake

Stopping after finding one common prime factor (e.g. just 3 or just 7) and not multiplying together all the shared prime factors.

Assessment Objectives (question level, Edexcel 1MA1 spec — not per step)

AO1 Use standard techniques — 50%
AO2 Reason and communicate — 25%
AO3 Solve problems — 25%
Q2 Higher 2 marks
Edexcel 1MA1 · 2022

Question

Work out the lowest common multiple (LCM) of 24 and 56

Worked Solution

  1. Find the prime factors of 24: 24 = 2³ × 3.

  2. Find the prime factors of 56: 56 = 2³ × 7.

  3. The LCM uses each prime factor the greatest number of times it appears in either number: 2³ × 3 × 7 = 8 × 21 = 168.

Final Answer

168

Common Mistake

Confusing LCM with HCF — the LCM is found by taking the highest power of each prime factor (and multiplying them), while the HCF uses only the shared factors.

Assessment Objectives (question level, Edexcel 1MA1 spec — not per step)

AO1 Use standard techniques — 40%
AO2 Reason and communicate — 30%
AO3 Solve problems — 30%
Q3 Higher 2 marks
Edexcel 1MA1 · 2022

Question

Two numbers m and n are such that m is a multiple of 5, n is an even number, and the highest common factor (HCF) of m and n is 7. Write down a possible value for m and a possible value for n.

Worked Solution

  1. Since HCF(m, n) = 7, both m and n must be divisible by 7.

  2. m must also be a multiple of 5, so m must be divisible by both 5 and 7. The smallest such value is 5 × 7 = 35.

  3. n must be an even number divisible by 7. The smallest such value is 2 × 7 = 14.

  4. Check: HCF(35, 14) = 7. ✓ m = 35 is a multiple of 5. ✓ n = 14 is even. ✓ One valid answer is m = 35, n = 14.

Final Answer

m = 35, n = 14 (or other valid pairs such as m = 35, n = 28, or m = 105, n = 14)

Common Mistake

Choosing values that share a common factor greater than 7 — for example m = 35 and n = 28 have HCF = 7, but m = 35 and n = 70 have HCF = 35, not 7.

Assessment Objectives (question level, Edexcel 1MA1 spec — not per step)

AO1 Use standard techniques — 40%
AO2 Reason and communicate — 30%
AO3 Solve problems — 30%

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