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Find the greatest common factor. $\newline$ $4x^3, 6x^2$ $\newline$ Write your answer as a constant times a product of single variables raised to exponents. $\newline$ $\_\_$

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GCF of monomials

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Q. Find the greatest common factor.

\newline

4x^3, 6x^2

\newline

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

\newline

\_\_

Factorization of $4x^3$ : First find the complete factorization of $4x^3$ . $\newline$ $4 = 2 \times 2$ $\newline$ $x^3 = x \times x \times x$ $\newline$ $4x^3 = 2 \times 2 \times x \times x \times x$
Factorization of $6x^2$ : Now, find the complete factorization of $6x^2$ . $\newline$ $6 = 2 \times 3$ $\newline$ $x^2 = x \times x$ $\newline$ $6x^2 = 2 \times 3 \times x \times x$
Find Greatest Common Factor: We found: $\newline$ $4x^3 = 2 \times 2 \times x \times x \times x$ $\newline$ $6x^2 = 2 \times 3 \times x \times x$ $\newline$ Find the greatest common factor of $4x^3$ and $6x^2$ . $\newline$ Common factors are $2$ , $x$ , and $x$ . $\newline$ $2 \times x \times x = 2x^2$ $\newline$ Greatest common factor: $2x^2$

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