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Find the greatest common factor. $\newline$ $9g^3, 6g^3$ $\newline$ 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

9g^3, 6g^3

\newline

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

\newline

\_\_

Find Factorization of $9g^3$ : First, we need to find the complete factorization of $9g^3$ . $9 = 3 \times 3$ $g^3 = g \times g \times g$ Therefore, $9g^3$ can be written as the product of its prime factors and variables as follows: $9g^3 = 3 \times 3 \times g \times g \times g$
Find Factorization of $6g^3$ : Next, we find the complete factorization of $6g^3$ . $\newline$ $6 = 2 \times 3$ $\newline$ $g^3 = g \times g \times g$ $\newline$ So, $6g^3$ can be written as the product of its prime factors and variables as follows: $\newline$ $6g^3 = 2 \times 3 \times g \times g \times g$
Compare and Find Common Factors: Now, we compare the factorizations to find the common factors: $\newline$ $9g^3 = 3 \times 3 \times g \times g \times g$ $\newline$ $6g^3 = 2 \times 3 \times g \times g \times g$ $\newline$ The common factors are $3$ , $g$ , $g$ , and $g$ . $\newline$ Multiplying these common factors together gives us the greatest common factor (GCF): $\newline$ GCF = $3 \times g \times g \times g = 3g^3$

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