Where can I download free prime factors hcf and lcm PDF worksheets with answers?

On this MathsLinks page you can download free printable prime factors hcf and lcm PDF worksheets (Qs) and full worked solutions or mark schemes (Ans) from Ken Stafford, Ken Stafford (1), Ken Stafford (2), Ken Stafford (3), IGCSE MT, plus a printable one-page prime factors hcf and lcm revision guide.

What GCSE grade is prime factors hcf and lcm (4C)?

Prime factors HCF and LCM (topic code 4C) is a Grade 4 number topic in GCSE Maths for Edexcel, AQA, OCR, Eduqas and IGCSE specifications.

Free Prime factors HCF and LCM Worksheets (PDF) with Answers — GCSE Maths

Free Prime factors HCF and LCM PDF Worksheets & Answers

Grade 4 • Topic 4C

Resource	Questions	Answers
Ken Stafford GCSE past paper questions & solutions	Qs	Ans
Ken Stafford (1) Practice worksheet & worked solutions	Qs	Ans
Ken Stafford (2) Practice worksheet & worked solutions	Qs	Ans
Ken Stafford (3) Practice worksheet & worked solutions	Qs	Ans
IGCSE MT IGCSE (9–1) past paper booklet	Qs	Ans
Maths Genie Graded exam questions & solutions	Qs	Ans
Maths4Everyone GCSE 9–1 practice booklet & solutions	Qs	Ans
Corbett Practice Practice Questions & answers	Qs	Ans
Corbett Textbook Textbook Exercise & answers	Qs	Ans
Maths Made Easy MME worksheet & model answers	Qs	Ans
Naiker Maths Exam question booklet & solutions	Qs	Ans
1st Class Maths (Edxl) Edexcel exam questions & solutions	Qs	Ans
1st Class Maths (AQA) AQA exam questions & solutions	Qs	Ans
Hannah Kettle Practice sheet & answers	Qs	Ans
Dr Austin Practice grid / worksheet & answers	Qs	Ans
GCSE Maths Rocket Practice questions & answers	Qs	Ans
GCSE Maths Rocket (1) Practice questions & answers	Qs	Ans
E Classroom GCSE topic booklet & answers	Qs	Ans
PMT (Edxl) Edexcel GCSE topic questions & solutions	Qs	Ans
PMT (AQA) AQA GCSE topic questions & solutions	Qs	Ans
PMT (IGCSE) Edexcel IGCSE topic questions & solutions	Qs	Ans
The Maths Room Online topic notes & examples	Page
Cognito Interactive online lesson & practice	Page
MathsPad interactive resource Interactive online resource	Open

Grade 4 topics
4A - Compound interest	4B - Indices (index laws)
4C - Prime factors HCF and LCM	4D - Real life graphs
4E - Inequalities on a number line	4F - Solving inequalities
4G - Forming and solving equations	4H - nth term of a linear sequence
4J - Expanding and factorising	4K - Pythagoras theorem
4L - Angles in parallel lines	4M - Angles in polygons
4N - Surface area	4P - Volume of a cuboid
4Q - Volume of a prism	4R - Bearings
4S - Cylinders	4T - Plans and elevations
4U - Scatter graphs	4V - Probability
4W - Averages from tables	4X - Reverse mean
4Y - Area of a trapezium	4Z - Loci and construction

Explanation:

To express a number as a product of its prime factors, use a factor tree to split it until every branch ends at a prime number (2, 3, 5, 7, 11, 13…), then write the primes multiplied together in index form (e.g. 2³ × 3 × 5).

To find the HCF and LCM of two numbers, put their prime factors into a Venn diagram: multiply the primes in the intersection (overlap) to get the HCF, and multiply all primes in both circles to get the LCM.

Example 1: Write 140 as a product of its prime factors in index form.

140 = 2 × 70

70 = 2 × 35

35 = 5 × 7

2² × 5 × 7

Example 2: Given 60 = 2² × 3 × 5 and 84 = 2² × 3 × 7, find the HCF and LCM.

HCF = 2×2×3 = 12

LCM = 12×5×7

= 420

Scanned GCSE Exam Questions & Worked Solutions

GCSE Past Paper Prime factors HCF and LCM Questions & Answers

10-Question Interactive Quiz More Past Paper Questions

Past Paper Example 1 GCSE Jun 2025 2F Q20 / 2H Q1 4 marks

Full Paper (PDF) • Mark Scheme (PDF)

Work out
(a) Express 250 as a product of its prime factors. (2)
(b) Find the lowest common multiple (LCM) of 30 and 25 (2)

(a) Express 250 as a product of its prime factors. [2 marks]

(b) Find the lowest common multiple (LCM) of 30 and 25 [2 marks]

Worked Solution & Mark Scheme (4 marks)

Part (a) Solution:

250 = 2 × 125 = 2 × 5³ M1 A1

Answer (a): 2 × 5³

Part (b) Solution:

30 = 2 × 3 × 5 M1
25 = 5²
LCM = 2 × 3 × 5² = 150 A1

Answer (b): 150

Past Paper Example 2 GCSE Nov 2023 1F Q20 / 1H Q3 4 marks

Full Paper (PDF) • Mark Scheme (PDF)

Work out
(a) Write 156 as a product of its prime factors. (2) (b) Find the highest common factor (HCF) of 156 and 130 (2)

(a) Write 156 as a product of its prime factors. [2 marks]

(b) Find the highest common factor (HCF) of 156 and 130 [2 marks]

Worked Solution & Mark Scheme (4 marks)

Part (a) Solution:

156 = 2 × 78 = 2 × 2 × 39 = 2² × 3 × 13 M1 A1

Answer (a): 2² × 3 × 13

Part (b) Solution:

130 = 2 × 5 × 13 M1
HCF = 2 × 13 = 26 A1

Answer (b): 26

Past Paper Example 3 Eduqas Nov 2018 2F Q23 7 marks

Full Paper (PDF) • Mark Scheme (PDF)

Gregor owns a restaurant.

(a) The diagram shows a circular place mat. [2 marks]

The radius of the circular place mat is 14 cm.
Calculate the circumference of the circular place mat.

(b) Gregor plans to buy some spoons and forks.
A bag of 24 spoons costs £19.95.
A box of 18 forks costs £15.55.
Bags and boxes cannot be split.
Gregor decides to buy the same number of spoons as forks.
He places an order to buy the smallest number of each that he can.
Complete the details on the order form shown below.
You must show all your working.
@@TABULAR₀@@ [5 marks]

Worked Solution & Mark Scheme (7 marks)

Part (a) Solution:

C = 2 * π * r = 2 * π * 14 = 28π ≈ 87.96 cm (or 2 * 3.14 * 14 = 87.92 cm). M1 A1

Answer (a): 87.96 cm (or 88 cm, 87.92 cm)

Part (b) Solution:

Smallest common multiple of 24 and 18 is 72 M1
Bags of spoons = 72 / 24 = 3 bags M1
Cost of spoons = 3 * 19.95 = £59.85 M1
Boxes of forks = 72 / 18 = 4 boxes M1
Cost of forks = 4 * 15.55 = £62.20
Total cost = 59.85 + 62.20 = £122.05. A1

Answer (b): 3 bags of spoons (£59.85), 4 boxes of forks (£62.20), Total = £122.05

← 4B Indices (index laws)

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Prime factors HCF and LCM

Free Prime factors HCF and LCM PDF Worksheets & Answers

Guide to Prime factors HCF and LCM: Explanation, Diagrams & Worked Examples

GCSE Past Paper Prime factors HCF and LCM Questions & Answers