What is the greatest common factor of x4 and x5? (1 point)

x4

x3

x2

x

To find the greatest common factor (GCF) of \( x^4 \) and \( x^5 \), we look for the highest power of \( x \) that divides both terms.

1. \( x^4 = x \cdot x \cdot x \cdot x \)
2. \( x^5 = x \cdot x \cdot x \cdot x \cdot x \)

The largest power of \( x \) that is a factor of both \( x^4 \) and \( x^5 \) is \( x^4 \).

**Answer:** The greatest common factor of \( x^4 \) and \( x^5 \) is:
\[
\boxed{x^4}
\]

Would you like more details on finding the GCF of monomials or have any other questions? 

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Here are five related questions to explore further:
1. What is the greatest common factor of \( x^3 \) and \( x^7 \)?
2. How do we find the GCF of two terms with coefficients, such as \( 2x^4 \) and \( 6x^5 \)?
3. What is the GCF of \( x^4y^3 \) and \( x^5y \)?
4. How would the answer change if we were finding the least common multiple (LCM) of \( x^4 \) and \( x^5 \)?
5. Can we find the GCF of three terms, like \( x^4 \), \( x^5 \), and \( x^6 \)?

**Tip:** The GCF of powers of a variable is determined by the smallest exponent that appears in each term.

What is the greatest common factor of x^4 and x^5?

Discover how to find the greatest common factor (GCF) of x^4 and x^5. This problem illustrates key algebraic concepts and provides a step-by-step solution suitable for middle school students.

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