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

9w^3, 6w

\newline

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

\newline

\_\_

Factorization of $9w^3$ : First, find the complete factorization of $9w^3$ . $9 = 3 \times 3$ $w^3 = w \times w \times w$ Therefore, $9w^3 = 3 \times 3 \times w \times w \times w$ .
Factorization of $6w$ : Next, find the complete factorization of $6w$ . $\newline$ $6 = 2 \times 3$ $\newline$ $w = w$ $\newline$ Therefore, $6w = 2 \times 3 \times w$ .
Find Greatest Common Factor: Now, find the greatest common factor of $9w^3$ and $6w$ . The common factors are $3$ and $w$ . The greatest common factor is the product of the lowest powers of common factors, which is $3 \times w$ .
Write as Constant Times Variables: Write the greatest common factor as a constant times a product of single variables raised to exponents. $\newline$ The greatest common factor is $3w^1$ , which can also be written as $3w$ .

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