Find the GCF for the list.
98 a cubed b Superscript 6 Baseline c Superscript 4 Baseline comma 28 a Superscript 4 Baseline b


To find the Greatest Common Factor (GCF) for the given list of terms, we need to compare both the coefficients (numerical parts) and the variable parts.

### Step 1: Find the GCF of the numerical coefficients.
The numerical coefficients in the terms are 98 and 28.

- **98** can be factored as \( 2 \times 7^2 \).
- **28** can be factored as \( 2^2 \times 7 \).

The GCF of 98 and 28 is \( 2 \times 7 = 14 \).

### Step 2: Find the GCF of the variable parts.
- For \( a^3 \) and \( a^4 \), the GCF is \( a^3 \) (take the lowest exponent of \( a \)).
- For \( b^6 \) and \( b \), the GCF is \( b^1 = b \) (take the lowest exponent of \( b \)).
- For \( c^4 \) and the second term, which has no \( c \) (i.e., \( c^0 \)), the GCF is \( c^0 = 1 \).

### Step 3: Combine the GCFs.
The overall GCF is the product of the GCFs found in steps 1 and 2:

\[
\text{GCF} = 14 \times a^3 \times b \times 1 = 14a^3b
\]

So, the GCF of \( 98a^3b^6c^4 \) and \( 28a^4b \) is **14a³b**.

Would you like more details, or do you have any questions? 

Here are 5 related questions to consider:
1. How do you find the GCF of a polynomial with multiple terms?
2. What is the process of finding the GCF of three or more terms?
3. Can the GCF include fractional or decimal coefficients?
4. How does the GCF relate to factoring polynomials?
5. What happens if there is no common factor between the terms?

**Tip:** Always break down each component separately (coefficients and variables) when finding the GCF in algebraic expressions.

Learn how to find the Greatest Common Factor (GCF) of 98a³b⁶c⁴ and 28a⁴b using step-by-step explanations. This problem involves polynomials and exponents, focusing on identifying common factors in algebraic expressions. Suitable for students in Grades 9-12.

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