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Find the greatest common factor. $\newline$ $10v^3, 8v^3$ $\newline$ 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

10v^3, 8v^3

\newline

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

\newline

\_\_

Factorization of $10v^3$ : First find the complete factorization of $10v^3$ . $\newline$ $10 = 2 \times 5$ $\newline$ $v^3 = v \times v \times v$ $\newline$ $10v^3 = 2 \times 5 \times v \times v \times v$
Factorization of $8v^3$ : Now, find the complete factorization of $8v^3$ . $\newline$ $8 = 2 \times 2 \times 2$ $\newline$ $v^3 = v \times v \times v$ $\newline$ $8v^3 = 2 \times 2 \times 2 \times v \times v \times v$
Common Factor Calculation: We found: $\newline$ $10v^3 = 2 \times 5 \times v \times v \times v$ $\newline$ $8v^3 = 2 \times 2 \times 2 \times v \times v \times v$ $\newline$ Find the greatest common factor of $10v^3$ and $8v^3$ . $\newline$ The common factors are $2$ , $v$ , $v$ , and $v$ . $\newline$ $2 \times v \times v \times v = 2v^3$ $\newline$ Greatest common factor: $2v^3$

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