Definition of Greatest Common Factor (GCF) in algebraic expressions for Grade 7 math.

📚 Quick Study Guide

• 🔢 Definition: The Greatest Common Factor (GCF) of two or more algebraic expressions is the largest factor that divides each expression completely.
• ➗ Finding the GCF (Numbers): Find the largest number that divides all the numerical coefficients. For example, the GCF of 12 and 18 is 6.
• 🧮 Finding the GCF (Variables): Identify common variables and select the lowest power of each variable. For example, the GCF of $x^3$ and $x^2$ is $x^2$.
• 💡 Combining Numbers and Variables: Combine the GCF of the numerical coefficients and the GCF of the variables. For example, the GCF of $12x^3$ and $18x^2$ is $6x^2$.
• 📝 Example: Find the GCF of $15a^2b$ and $25ab^2$. The GCF of 15 and 25 is 5. The GCF of $a^2$ and $a$ is $a$. The GCF of $b$ and $b^2$ is $b$. Therefore, the GCF of $15a^2b$ and $25ab^2$ is $5ab$.

Practice Quiz

1. What is the GCF of $6x$ and $9y$?
   1. 3
   2. $x$
   3. $y$
   4. $3xy$
2. What is the GCF of $12a^2$ and $18a$?
   1. $6a^2$
   2. $12a$
   3. $6a$
   4. $18a$
3. What is the GCF of $5x^3$ and $10x^2$?
   1. $5x^3$
   2. $10x^2$
   3. $5x^2$
   4. $x^2$
4. What is the GCF of $8p^4q$ and $16pq^2$?
   1. $8p^4q$
   2. $16pq^2$
   3. $8pq$
   4. $4pq$
5. What is the GCF of $21m^2n^3$ and $14mn^2$?
   1. $7mn^2$
   2. $7m^2n^3$
   3. $14mn^2$
   4. $21m^2n^3$
6. What is the GCF of $3ab^2c$ and $9a^2bc$?
   1. $3a^2bc$
   2. $9ab^2c$
   3. $3abc$
   4. $abc$
7. What is the GCF of $4x^2y^3z$ and $6xy^2z^2$?
   1. $2x^2y^3z$
   2. $2xy^2z$
   3. $6xy^2z^2$
   4. $4x^2y^3z$