📚 Topic Summary
Finding the Greatest Common Factor (GCF) of monomials is a fundamental skill in Algebra 1. The GCF is the largest factor that divides evenly into two or more monomials. To find the GCF, determine the GCF of the coefficients (the numerical parts) and then identify the lowest power of each common variable. Combining these gives you the GCF of the monomials.
For example, consider $12x^2y$ and $18xy^3$. The GCF of 12 and 18 is 6. The lowest power of $x$ is $x^1$ (or simply $x$), and the lowest power of $y$ is $y^1$ (or simply $y$). Therefore, the GCF of $12x^2y$ and $18xy^3$ is $6xy$.
🧠 Part A: Vocabulary
Match the term with its correct definition:
| Term |
Definition |
| 1. Monomial |
A. The largest factor that divides evenly into two or more terms. |
| 2. Coefficient |
B. A term that contains only numbers, variables, and nonnegative integer exponents. |
| 3. Variable |
C. A symbol (usually a letter) that represents a value. |
| 4. Exponent |
D. The numerical factor of a term. |
| 5. GCF |
E. A quantity representing the power to which a given number or expression is to be raised. |
✏️ Part B: Fill in the Blanks
The GCF of monomials involves finding the largest common ______ of the coefficients and the lowest ______ of common variables. For example, to find the GCF of $24a^3b^2$ and $36a^2b^4$, we first find the GCF of 24 and 36, which is ______. Then, we identify the lowest power of $a$, which is ______, and the lowest power of $b$, which is ______. Therefore, the GCF of $24a^3b^2$ and $36a^2b^4$ is $12a^2b^2$.
🤔 Part C: Critical Thinking
Explain in your own words how finding the GCF of monomials can be helpful in simplifying algebraic expressions. Provide an example.