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Find the greatest common factor. $\newline$ $8r^3, 6$ $\newline$ 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

8r^3, 6

\newline

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

\newline

\_\_

Factorization of $8r^3$ : First find the complete factorization of $8r^3$ . $\newline$ $8 = 2 \times 2 \times 2$ $\newline$ $r^3 = r \times r \times r$ $\newline$ $8r^3 = 2 \times 2 \times 2 \times r \times r \times r$
Factorization of $6$ : Now, find the complete factorization of $6$ . $6 = 2 \times 3$ $6$ has no variable part, so it is just the product of its prime factors.
Find Greatest Common Factor: We found: $\newline$ $8r^3 = 2 \times 2 \times 2 \times r \times r \times r$ $\newline$ $6 = 2 \times 3$ $\newline$ Find the greatest common factor of $8r^3$ and $6$ . $\newline$ The only common factor between the two expressions is $2$ .
Final Result: Since there are no common variable factors and the only common constant factor is $2$ , the greatest common factor is $2$ .

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