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Find the greatest common factor. $\newline$ $10k, 6k^3$ $\newline$ 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

10k, 6k^3

\newline

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

\newline

\_\_

Factorization of $10$ k: First find the complete factorization of $10$ k. $\newline$ $10 = 2 \times 5$ $\newline$ $k = k$ $\newline$ $10k = 2 \times 5 \times k$
Factorization of $6k^3$ : Now, find the complete factorization of $6k^3$ . $6 = 2 \times 3$ $k^3 = k \times k \times k$ $6k^3 = 2 \times 3 \times k \times k \times k$
Find Greatest Common Factor: We found: $\newline$ $10k = 2 \times 5 \times k$ $\newline$ $6k^3 = 2 \times 3 \times k \times k \times k$ $\newline$ Find the greatest common factor of $10k$ and $6k^3$ . $\newline$ Common factors are $2$ and $k$ . $\newline$ $2 \times k = 2k$ $\newline$ Greatest common factor: $2k$

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