Find the greatest common factor of the following list of terms.

18 x Superscript 6 Baseline y Superscript 618x6y6​, 

16 x squared y cubed16x2y3​, 

and 14 x Superscript 4 Baseline y squared14x4y2

To find the greatest common factor (GCF) of the given terms, we'll follow a similar process by finding the GCF of both the numerical coefficients and the variables.

Given terms:
1. \( 18x^6y^6 \)
2. \( 16x^2y^3 \)
3. \( 14x^4y^2 \)

### Step 1: Find the GCF of the numerical coefficients.

- The coefficients are 18, 16, and 14.
- The factors of 18 are \( 1, 2, 3, 6, 9, 18 \).
- The factors of 16 are \( 1, 2, 4, 8, 16 \).
- The factors of 14 are \( 1, 2, 7, 14 \).

The greatest common factor of 18, 16, and 14 is **2**.

### Step 2: Find the GCF of the variables \( x \) and \( y \).

- For \( x^6 \), \( x^2 \), and \( x^4 \), the smallest power is \( x^2 \).
- For \( y^6 \), \( y^3 \), and \( y^2 \), the smallest power is \( y^2 \).

### Step 3: Multiply the GCF of the coefficients and the variables.

The GCF is the product of the GCF of the coefficients and the lowest powers of the variables:
\[
\text{GCF} = 2 \cdot x^2 \cdot y^2 = 2x^2y^2
\]

So, the greatest common factor is **\( 2x^2y^2 \)**.

Would you like any additional details? Here are some related questions:

1. How can you factor a polynomial using the greatest common factor?
2. What is the difference between the GCF of numbers and the GCF of algebraic terms?
3. How would you find the GCF of terms that include more variables?
4. How does finding the GCF help in simplifying algebraic fractions?
5. Can the concept of GCF be applied to polynomials with non-integer coefficients?

**Tip:** Always break down both the numerical and variable components separately to find the GCF in algebraic expressions.

Discover how to find the greatest common factor (GCF) of 18x^6y^6, 16x^2y^3, and 14x^4y^2. This problem involves identifying the GCF of numerical coefficients and variables in algebraic expressions. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation