Prime Factor Method: Error Analysis & Misconceptions
Mathematics
Grade 8
12 questions
~24 mins
1 views0 downloads
About This Worksheet
A worksheet focusing on the Prime Factor Method for calculating HCF, designed to address common misconceptions and reinforce understanding among Grade 8 students.
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Prime Factor Method: Error Analysis & Misconceptions
Subject: MathematicsGrade: Grade 8
Name:
Date:
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Untitled Worksheet
Grade Grade 8
A
Fluency & Practice
Answer all questions. Show your working in the grid spaces provided.
1.
Prime factorize 48 and 60. What is their HCF using the Prime Factor Method?
[3 marks]2.
Find the HCF of 84 and 126 by listing their prime factors.
[3 marks]3.
Prime factorize 36 and 54. Identify the common prime factors and find their HCF.
[3 marks]4.
Calculate the HCF of 120 and 150 using prime factors.
[3 marks]B
Problem Solving & Reasoning
Answer all questions. Show detailed working using prime factors.
1.
Two numbers have a common prime factor of 3, and their prime factorizations include 2² and 3¹. Find the HCF and explain your reasoning.
[4 marks]2.
Explain why the HCF of 48 and 80 is 16, using their prime factorization.
[4 marks]3.
If the HCF of two numbers is 24, and one number is 36, what is the other number if it shares no larger common factors? Justify your answer.
[4 marks]C
Real-world Applications
Complete the word problems below, showing your prime factorization and reasoning.
1.
A school is dividing students into groups. One group has 84 students and another 126 students. Find the largest number of groups that can be formed so that each group has the same number of students, using the Prime Factor Method.
[4 marks]D
Challenge & Extension
Attempt these advanced problems. Show all working.
1.
Find the HCF of 210 and 350 using prime factors. Then, verify your answer by division.
[4 marks]2.
Given two numbers with prime factorizations 2³×3²×5 and 2²×3×7, find their HCF and explain how the prime factor method helps in this calculation.
[4 marks]E
Mixed Review & Error Analysis
Review these questions carefully. Some common mistakes are shown. Identify the errors and correct them.
1.
A student prime factorizes 48 as 2⁶ and 3, then concludes the HCF of 48 and 60 is 48. Identify the mistake and find the correct HCF.
[4 marks]2.
Another student incorrectly states that the HCF of 36 and 54 is 18 because both are divisible by 6. Explain why this is incorrect when using prime factors.
[4 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.
- • Change grade level (Grade 6 → Grade 7)
- • Swap topics (Harry Potter → Macbeth)
- • Add more questions (10 → 15)
- • Adjust difficulty
Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet