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What is the greatest common factor of
54z^(3),18 z, and
36z^(2) ?

What is the greatest common factor of $54 z^{3}, 18 z$ , and $36 z^{2}$ ?

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Greatest common factor of three or four numbers

Full solution

Q. What is the greatest common factor of

54 z^{3}, 18 z

, and

36 z^{2}

?

List Prime Factors: List the prime factors of each term. $\newline$ $54z^{3}$ can be factored into $2 \times 3^3 \times z^3$ . $\newline$ $18z$ can be factored into $2 \times 3^2 \times z$ . $\newline$ $36z^{2}$ can be factored into $2^2 \times 3^2 \times z^2$ .
Identify Common Factors: Identify the common prime factors. $\newline$ The common prime factors of $54z^{3}$ , $18z$ , and $36z^{2}$ are $2$ and $3^2$ (since $3^2$ is the lowest power of $3$ that appears in all three terms) and $z$ (since $z$ is the lowest power of $z$ that appears in all three terms).
Calculate GCF: Calculate the greatest common factor (GCF). $\newline$ The GCF is the product of the lowest powers of the common prime factors. $\newline$ GCF = $2 \times 3^2 \times z = 2 \times 9 \times z = 18z$ .

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