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Find the greatest common factor. $\newline$ $6k^2, 9k^2$ $\newline$ 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

6k^2, 9k^2

\newline

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

\newline

______

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

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