Question
Find the greatest common factor. \( 2 q, 4 q \) Write your answer as a constant times a product of single variables raised to exponents.
Ask by Reeves Valdez. in the United States
Feb 02,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The greatest common factor is \( 2q \).
Solution
To find the **Greatest Common Factor (GCF)** of the terms \( 2q \) and \( 4q \), follow these steps:
1. **Factor Each Term:**
- \( 2q = 2 \times q \)
- \( 4q = 4 \times q = 2^2 \times q \)
2. **Identify Common Factors:**
- Both terms have the factor \( 2 \) and \( q \).
3. **Determine the Lowest Exponents for Common Factors:**
- For \( 2 \): The lowest exponent is \( 1 \) (from \( 2q \)).
- For \( q \): The lowest exponent is \( 1 \) (both terms have \( q \)).
4. **Multiply the Common Factors with Their Lowest Exponents:**
\[
\text{GCF} = 2^1 \times q^1 = 2q
\]
**Final Answer:**
\[
2q
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Beyond the Answer
The greatest common factor (GCF) of \( 2q \) and \( 4q \) is \( 2q \). To find the GCF, we look at the coefficients first: the GCF of 2 and 4 is 2. For the variable \( q \), it appears in both terms as \( q^1 \). Therefore, we combine them to get \( 2q^1 \), which can also be simply written as \( 2q \). Now, isn't it fun how factors play a role in everything from simplifying fractions to solving equations? Understanding the GCF can make your life easier in algebra and beyond! Just think of it like being the best negotiator in a group of friends—finding common ground is key!
