Finding the Greatest Common Factor (GCF)
Finding the Greatest Common Factor Using Different Methods
Learning Standards
Content Standard
The learner demonstrates understanding of factors, multiples, and divisibility rules
Performance Standard
The learner is able to apply divisibility rules and find GCF and LCM in problem solving
Learning Competency
Find the Greatest Common Factor (GCF) of two or more numbers using listing, prime factorization, and continuous division
Code: M6NS-Ic-71
Complete Lesson Plan
Learning Objectives
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Define Greatest Common Factor (GCF)
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Find the GCF using the listing method
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Find the GCF using prime factorization
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Find the GCF using continuous division
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Solve problems involving GCF
Lesson Procedures
motivation
Real-life Problem: 'You have 12 red balloons and 18 blue balloons. You want to arrange them in groups with the same number in each group. What is the largest number of balloons you can put in each group?'
presentation
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Problem: Find the GCF of 12 and 18
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Method 1: Listing Method
- Factors of 12: 1, 2, 3, 4, 6, 12
- Factors of 18: 1, 2, 3, 6, 9, 18
- Common factors: 1, 2, 3, 6
- GCF = 6 (greatest common factor)
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Method 2: Prime Factorization
- 12 = 2 × 2 × 3 = 2² × 3
- 18 = 2 × 3 × 3 = 2 × 3²
- Common prime factors: 2 × 3 = 6
- GCF = 6
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Method 3: Continuous Division
2 | 12 18 3 | 6 9 | 2 3Multiply divisors: 2 × 3 = 6 GCF = 6
generalization
Questions:
- What is GCF?
- What are the three methods for finding GCF?
- Which method is fastest for large numbers?
- How is GCF useful in real life?
guided practice
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Find GCF of 24 and 36 using all three methods:
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Listing:
- 24: 1, 2, 3, 4, 6, 8, 12, 24
- 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
- GCF = 12
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Prime Factorization:
- 24 = 2³ × 3
- 36 = 2² × 3²
- Common: 2² × 3 = 12
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Continuous Division:
2 | 24 36 2 | 12 18 3 | 6 9 | 2 3GCF = 2 × 2 × 3 = 12
independent practice
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Activity 1: Find the GCF using any method:
- GCF of 16 and 24 = ____
- GCF of 30 and 45 = ____
- GCF of 20, 30, and 40 = ____
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Activity 2: Solve: Maria has 48 chocolates and 36 candies. She wants to pack them in bags with equal amounts. What is the greatest number of items she can put in each bag?
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Activity 3: Use Venn diagram to find GCF of 18 and 27
preliminary activities
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Prayer and greetings
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Review: Listing factors of numbers
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Quick drill: Find all factors of 12, 18, 24
Assessment
answers
- 7
- 16
- 5
- 18
- GCF(60, 84) = 12 fruits per basket
evaluation
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Find the GCF:
- GCF of 14 and 21 = ____
- GCF of 32 and 48 = ____
- GCF of 15, 25, and 35 = ____
- Use continuous division to find GCF of 54 and 72
- Word Problem: A farmer has 60 mangoes and 84 bananas. He wants to arrange them in baskets with equal number of fruits. What is the greatest number of fruits he can put in each basket?
Materials & Resources
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Factor cards
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Venn diagram charts
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Multiplication table
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Manila paper and colored markers
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Prime factorization worksheets
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Continuous division practice sheets
assignment
Homework:
- Find GCF of: (a) 28 and 42, (b) 36 and 60, (c) 18, 24, and 30
- Create your own word problem involving GCF
- Practice all three methods with different number pairs
Remarks:
- Emphasize the practical applications of GCF
- Encourage students to check their answers using different methods
subject matter
Topic: Greatest Common Factor (GCF)
Key Concepts:
- Greatest Common Factor (GCF) is the largest number that divides two or more numbers evenly
- Also called Greatest Common Divisor (GCD)
- Three methods to find GCF:
- Listing Method - list all factors and find the greatest common one
- Prime Factorization - use prime factors common to all numbers
- Continuous Division - divide by common factors until no common factor remains
Materials:
- Factor cards
- Venn diagram charts
- Multiplication table
- Manila paper
- Colored markers