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Find the greatest common factor. $\newline$ $6m^2, 9m^2$ $\newline$ Write your answer as a constant times a product of single variables raised to exponents. $\newline$ $\_\_$

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GCF of monomials

Full solution

Q. Find the greatest common factor.

\newline

6m^2, 9m^2

\newline

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

\newline

\_\_

Factorization of $6m^2$ : First find the complete factorization of $6m^2$ . $\newline$ $6 = 2 \times 3$ $\newline$ $m^2 = m \times m$ $\newline$ $6m^2 = 2 \times 3 \times m \times m$
Factorization of $9m^2$ : Now, find the complete factorization of $9m^2$ . $\newline$ $9 = 3 \times 3$ $\newline$ $m^2 = m \times m$ $\newline$ $9m^2 = 3 \times 3 \times m \times m$
Common Factor Calculation: We found: $\newline$ $6m^2 = 2 \times 3 \times m \times m$ $\newline$ $9m^2 = 3 \times 3 \times m \times m$ $\newline$ Find the greatest common factor of $6m^2$ and $9m^2$ . $\newline$ Common factors are $3$ , $m$ , and $m$ . $\newline$ $3 \times m \times m = 3m^2$ $\newline$ Greatest common factor: $3m^2$

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