Algebra 1 GCF of Monomials Exam Questions

📚 Quick Study Guide

• 🔢 Greatest Common Factor (GCF): The largest factor that divides two or more monomials without leaving a remainder.
• 💡 Prime Factorization: Break down each monomial into its prime factors. For example, $12x^2y = 2 \cdot 2 \cdot 3 \cdot x \cdot x \cdot y$.
• 🔍 Identify Common Factors: Find the factors that are common to all monomials.
• ➕ Determine the Lowest Exponent: For each common variable, choose the lowest exponent present in the monomials.
• 📝 Construct the GCF: Multiply the common factors (with their lowest exponents) to obtain the GCF.
• ➗ Dividing Monomials: When dividing monomials, divide the coefficients and subtract the exponents of like variables: $\frac{ax^m}{bx^n} = \frac{a}{b}x^{m-n}$.
• 📌 Example: Find the GCF of $12x^2y$ and $18xy^3$. Prime factors: $12x^2y = 2^2 \cdot 3 \cdot x^2 \cdot y$ and $18xy^3 = 2 \cdot 3^2 \cdot x \cdot y^3$. Common factors: $2$, $3$, $x$, and $y$. Lowest exponents: $x^1$ and $y^1$. GCF: $2 \cdot 3 \cdot x \cdot y = 6xy$.

Practice Quiz

1. What is the GCF of $15a^3b^2$ and $25a^2b^4$?
   1. $5a^2b^2$
   2. $5a^3b^4$
   3. $25a^3b^4$
   4. $15a^3b^2$
2. What is the GCF of $36x^4y^3z$ and $48x^2yz^2$?
   1. $12x^2yz$
   2. $12x^4y^3z^2$
   3. $36x^4y^3z$
   4. $48x^2yz^2$
3. What is the GCF of $14p^5q^2$ and $21p^3q^5$?
   1. $7p^3q^2$
   2. $7p^5q^5$
   3. $14p^5q^2$
   4. $21p^3q^5$
4. What is the GCF of $8m^6n^4$ and $20m^2n^7$?
   1. $4m^2n^4$
   2. $4m^6n^7$
   3. $20m^2n^7$
   4. $8m^6n^4$
5. What is the GCF of $9u^3v^5$ and $12u^4v^2$?
   1. $3u^3v^2$
   2. $3u^4v^5$
   3. $9u^3v^5$
   4. $12u^4v^2$
6. What is the GCF of $16r^2s^6$ and $24r^5s^3$?
   1. $8r^2s^3$
   2. $8r^5s^6$
   3. $16r^2s^6$
   4. $24r^5s^3$
7. What is the GCF of $5x^7y^2$, $10x^3y^5$, and $15x^4y^3$?
   1. $5x^3y^2$
   2. $5x^7y^5$
   3. $15x^4y^3$
   4. $10x^3y^5$