Common Factors: Real-world Applications
Mathematics
Year 9
12 questions
~24 mins
1 views0 downloads
About This Worksheet
A worksheet focusing on understanding and applying common factors to simplify fractions and solve real-world problems involving factors.
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Full preview • 12 questions
Common Factors: Real-world Applications
Subject: MathematicsGrade: Year 9
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Untitled Worksheet
Grade Year 9
A
Fluency & Practice
Answer all questions. Show your working in the grid spaces provided.
1.
Find the greatest common factor (GCF) of 48 and 60.
[2 marks]2.
Simplify the fraction 36/54 using common factors.
[2 marks]3.
Calculate the GCF of 81 and 99.
[2 marks]B
Problem Solving & Reasoning
Solve the problems step-by-step and explain your reasoning.
1.
A baker divides 120 cookies into packages with equal numbers, and each package contains 15 cookies. How many different ways can the baker package the cookies based on common factors?
[4 marks]2.
A school has 72 students and 90 chairs. Find the largest number of groups that can be formed with equal students and chairs in each group.
[3 marks]C
Real-world Applications
Apply your understanding of common factors to these real-world scenarios.
1.
A fabric store cuts cloth into pieces of equal length. If the total length of cloth is 144 meters and each piece is 24 meters long, how many pieces can be cut, and what is the greatest number of pieces that can be cut with equal length?
[3 marks]2.
A gardener has 96 tulips and 60 roses. He wants to plant them in flower beds with an equal number of tulips and roses in each bed, using the maximum possible number of beds. How many tulips and roses will each bed have?
[3 marks]D
Challenge & Extension
Attempt these more difficult problems to extend your understanding.
1.
Prove that the GCF of two numbers, 84 and 126, is 42 by listing all their factors and identifying the greatest common one.
[4 marks]2.
Find three pairs of numbers between 1 and 100 where the GCF is exactly 12, and explain your choices.
[4 marks]E
Mixed Review
Answer these questions to review various aspects of common factors.
1.
Identify the common factors of 45 and 75.
[2 marks]2.
Simplify the fraction 150/200 using their common factors.
[2 marks]F
Error Analysis
Review the following mistake and identify what was wrong and how to correct it.
1.
A student finds the GCF of 36 and 48 as 12 by listing factors. They conclude that 12 is the GCF because it is the largest number common to both lists. Is this correct? Why or why not?
[3 marks]Quick Actions
What is Remix?
Create a new worksheet based on this one. Change the grade level, topic, number of questions, or difficulty - then generate a fresh version.
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Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet