Pregunta
Find the greatest common factor. \[ 2 m^{3}, 6 m^{3} \]
Ask by Santiago Guzman. in the United States
Mar 13,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
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The greatest common factor is \( 2m^3 \).
Solución
1. Write down the two expressions:
\[
2m^3 \quad \text{and} \quad 6m^3.
\]
2. Find the greatest common factor (GCF) of the numerical coefficients:
\[
\text{GCF}(2, 6) = 2.
\]
3. For the variable part \( m^3 \) in both expressions, the GCF is \( m^3 \) (since both have the same power).
4. Multiply the GCF of the coefficients and the variable:
\[
2 \times m^3 = 2m^3.
\]
Thus, the greatest common factor is:
\[
\boxed{2m^3}.
\]
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Simplifique esta solución Bonus Knowledge
To find the greatest common factor (GCF) of \(2m^3\) and \(6m^3\), start by factoring each term. The term \(2m^3\) can be factored into \(2 \cdot m^3\), and \(6m^3\) can be factored into \(2 \cdot 3 \cdot m^3\). The GCF is determined by identifying the lowest powers of each factor: the GCF of the coefficients 2 and 6 is 2, and the GCF of \(m^3\) is \(m^3\) itself. So, the GCF is \(2m^3\). The greatest common factor of \(2m^3\) and \(6m^3\) is \(2m^3\). Enjoy using this knowledge to simplify expressions and solve problems!
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