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Find the greatest common factor. $\newline$ $5z^3, 10z$ $\newline$ 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

5z^3, 10z

\newline

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

\newline

\_\_

Factorization of $5z^3$ : First find the complete factorization of $5z^3$ . $\newline$ $5$ is a prime number, so it cannot be factored further. $\newline$ $z^3 = z \times z \times z$ $\newline$ Therefore, the complete factorization of $5z^3$ is: $\newline$ $5z^3 = 5 \times z \times z \times z$
Factorization of $10$ z: Now, find the complete factorization of $10z$ . $10 = 2 \times 5$ $z$ is already a single variable with an exponent of $1$ .So, the complete factorization of $10z$ is: $10z = 2 \times 5 \times z$
Common Factor Calculation: We found: $\newline$ $5z^3 = 5 \times z \times z \times z$ $\newline$ $10z = 2 \times 5 \times z$ $\newline$ Find the greatest common factor of $5z^3$ and $10z$ . $\newline$ The common factors are $5$ and $z$ . $\newline$ The greatest common factor is the product of these common factors. $\newline$ Greatest common factor: $5z$

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