What is the GCF of h^4 and h^8?
Understand the Problem
The question is asking for the greatest common factor (GCF) of the expressions h4 and h8. To find the GCF, we need to identify the highest power of 'h' that appears in both terms.
Answer
The GCF is $h^4$.
Answer for screen readers
The greatest common factor (GCF) is $h^4$.
Steps to Solve
- Identify the expressions
The expressions given are $h^4$ and $h^8$.
- Find the powers of h
Identify the powers of $h$ in each expression. We have:
- From $h^4$, the power is 4.
- From $h^8$, the power is 8.
- Determine the GCF
The GCF is found by taking the lowest of the powers. Thus, we take the minimum of 4 and 8: $$ \text{GCF} = h^{\min(4, 8)} = h^4 $$
The greatest common factor (GCF) is $h^4$.
More Information
The GCF is useful in simplifying fractions and factoring expressions. In this case, $h^4$ is the highest power of $h$ that divides both $h^4$ and $h^8$.
Tips
- A common mistake is to confuse the GCF with the least common multiple (LCM), which would require identifying the highest powers instead of the lowest.
- Another mistake is to forget to include the variable when stating the GCF.
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