Greatest Common Factor (GCF)
Greatest Common Factor (GCF) can be found by listing all factors or by using prime factorization. In Grade 6 Saxon Math Course 1, the prime-factorization method identifies common prime factors between two numbers and multiplies them together. For GCF(24, 36): 24 = 2³ × 3 and 36 = 2² × 3², so GCF = 2² × 3 = 12. The listing method checks factor lists for the largest shared factor. Both methods give identical results; prime factorization is more efficient for larger numbers.
Key Concepts
New Concept The greatest common factor (GCF) is the largest whole number that is a factor of two or more given numbers. What’s next This is just the foundation. Next, you'll tackle worked examples to see the process in action and then test your skills on various problem sets.
Common Questions
What is the GCF of 24 and 36 using prime factorization?
24 = 2³ × 3, 36 = 2² × 3². Shared factors: 2² and 3¹. GCF = 4 × 3 = 12.
How does the listing method find GCF?
List all factors of each number, identify shared factors, and pick the largest. For 12 and 18: factors of 12 are {1,2,3,4,6,12}, factors of 18 are {1,2,3,6,9,18}, shared are {1,2,3,6}, GCF = 6.
Why is prime factorization more efficient for large numbers?
Listing all factors of large numbers is time-consuming. Prime factorization directly identifies which prime factors are shared, making GCF computation faster.
GCF(48, 72) = ?
48 = 2⁴ × 3, 72 = 2³ × 3². Shared: 2³ × 3 = 24.
How is GCF used in fraction simplification?
Divide both numerator and denominator by their GCF to reduce the fraction to lowest terms in one step.