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Find the greatest common factor. $\newline$ $2r^2, 3r^2$ $\newline$ 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

2r^2, 3r^2

\newline

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

\newline

______

Factorization of $2r^2$ : First find the complete factorization of $2r^2$ . $\newline$ $2 = 2$ $\newline$ $r^2 = r \times r$ $\newline$ $2r^2 = 2 \times r \times r$
Factorization of $3r^2$ : Now, find the complete factorization of $3r^2$ . $\newline$ $3 = 3$ $\newline$ $r^2 = r \times r$ $\newline$ $3r^2 = 3 \times r \times r$
Common Factor of $2r^2$ and $3r^2$ : We found: $\newline$ $2r^2 = 2 \times r \times r$ $\newline$ $3r^2 = 3 \times r \times r$ $\newline$ Find the greatest common factor of $2r^2$ and $3r^2$ . $\newline$ The only common factors are $r$ and $r$ because the constants $2$ and $3$ are different prime numbers and have no common factors. $\newline$ $3r^2$ $0$ $\newline$ Greatest common factor: $3r^2$ $1$

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