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Find the greatest common factor. $\newline$ $2g^3, 4g^2$ $\newline$ Write your answer as a constant times a product of single variables raised to exponents. $\newline$ $\_\_$

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GCF of monomials

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Q. Find the greatest common factor.

\newline

2g^3, 4g^2

\newline

Write your answer as a constant times a product of single variables raised to exponents.

\newline

\_\_

Factorization of $2g^3$ : First find the complete factorization of $2g^3$ . $\newline$ $2 = 2$ $\newline$ $g^3 = g \cdot g \cdot g$ $\newline$ $2g^3 = 2 \cdot g \cdot g \cdot g$
Factorization of $4g^2$ : Now, find the complete factorization of $4g^2$ . $\$4 = 2 \times 2$ \) $\$g^2 = g \times g$ \) $\$4g^2 = 2 \times 2 \times g \times g$ \)
Find Greatest Common Factor: We found: $\newline$ $2g^3 = 2 \times g \times g \times g$ $\newline$ $4g^2 = 2 \times 2 \times g \times g$ $\newline$ Find the greatest common factor of $2g^3$ and $4g^2$ . $\newline$ Common factors are $2$ , $g$ , and $g$ . $\newline$ $2 \times g \times g = 2g^2$ $\newline$ Greatest common factor: $2g^2$

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