Greatest common factors
This Grade 6 algebra skill from Yoshiwara Elementary Algebra teaches students to find the greatest common factor (GCF) of two or more numbers or algebraic terms. Students use the GCF to factor expressions and simplify fractions, which is a foundational skill for polynomial factoring.
Key Concepts
Property The greatest common factor (GCF) is the largest factor that divides evenly into each term of the polynomial. It consists of the largest numerical factor and the highest power of each variable that is common to all terms. The exponent on each variable of the GCF is the smallest exponent that appears on that variable among the terms of the polynomial.
Examples For $15x^2y^2 12xy + 6xy^3$, the GCF of the coefficients 15, 12, and 6 is 3. The smallest power of $x$ is $x^1$ and of $y$ is $y^1$. The GCF is $3xy$.
To factor $4a^3b^2 + 6ab^3 18a^2b^4$, the GCF is $2ab^2$. Factoring this out gives $2ab^2(2a^2 + 3b 9ab^2)$.
Common Questions
What is the greatest common factor (GCF)?
The GCF of two or more numbers is the largest number that divides evenly into all of them. For example, the GCF of 12 and 18 is 6.
How do you find the GCF of two numbers?
List the factors of each number and find the largest one they share, or use prime factorization and multiply the common prime factors.
How do you factor out the GCF from a polynomial?
Find the GCF of all terms, then divide each term by the GCF. Write the result as GCF × (remaining terms). For example, 6x + 9 = 3(2x + 3).
Why is finding the GCF important in algebra?
Factoring out the GCF simplifies expressions and is the first step in fully factoring a polynomial.
Where is greatest common factor taught in Grade 6?
Greatest common factors are covered in the Yoshiwara Elementary Algebra textbook for Grade 6.