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Find the greatest common factor. $\newline$ $6b^3, 9b^2$ $\newline$ 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

6b^3, 9b^2

\newline

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

\newline

\_\_

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

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