Greatest Common Factor: Error Analysis & Misconceptions

Mathematics
Year 9
11 questions
~22 mins
1 views0 downloads

About This Worksheet

A worksheet focusing on identifying and correcting misconceptions related to the Greatest Common Factor (GCF), with a variety of question types to develop procedural fluency and reasoning skills.

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Greatest Common Factor: Error Analysis & Misconceptions

Subject: MathematicsGrade: Year 9
Name:
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Untitled Worksheet

Grade Year 9
A

Fluency & Practice

Calculate the Greatest Common Factor of the following pairs of numbers. Show your working in the grid spaces provided.
1.
Find the GCF of 24 and 36.
[2 marks]
2.
Calculate the GCF of 81 and 54.
[2 marks]
3.
Determine the GCF of 48 and 180.
[2 marks]
4.
Find the GCF of 50 and 75.
[2 marks]
B

Problem Solving & Reasoning

Solve the following multi-step problems involving GCF. Explain your reasoning clearly.
1.
A farmer has 120 apples and 150 oranges. She wants to pack them into boxes with an equal number of each fruit in each box, with no fruit left over. What is the maximum number of apples and oranges she can pack per box? Explain your process.
[4 marks]
2.
A school is dividing students into groups for two different activities. One activity has 36 students, and another has 48 students. They want to form groups with the same number of students, with no students left over. What is the largest possible group size? Show your working.
[4 marks]
3.
Two fractions, 18/24 and 30/45, need to be simplified to their lowest terms. Use GCF to simplify both fractions and verify the results.
[3 marks]
C

Real-world Applications

Apply your understanding of GCF to real-world context problems.
1.
A bakery makes 84 cookies and 126 muffins. They want to package them into boxes with the same number of each item, with no leftovers. What is the maximum number of cookies and muffins per box? Justify your answer.
[4 marks]
2.
A concert hall has 150 seats in one row and 180 seats in another. To reorganize, the manager wants to arrange seats into rows with the same number of seats, with no seats remaining. What is the greatest number of seats per row? Show your calculations.
[4 marks]
D

Challenge & Extension

Tackle these advanced problems involving GCF. Provide detailed explanations.
1.
Find three consecutive integers such that the GCF of the first and third integers is 6. Explain your reasoning and find the numbers.
[4 marks]
2.
Prove that 48 and 180 have a GCF of 12, and then determine the GCF of 48, 180, and 96. Explain each step.
[4 marks]

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Details

Created
1/1/2026
Updated
1/1/2026
Type
worksheet