Exponents and Polynomials
Greatest common factor of three univariate monomials

Find the greatest common factor of these three expressions.
\[
45 w^{3}, 30 w, \text { and } 75 w^{5}
\]

Answer

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Answer

\(\boxed{15w}\) is the final answer.

Steps

Step 1 ：Find the GCF of the coefficients 45, 30, and 75. The GCF is 15.

Step 2 ：Find the GCF of the variables \(w^{3}\), \(w\), and \(w^{5}\). The GCF is the one with the smallest exponent, which is \(w\).

Step 3 ：Therefore, the GCF of \(45w^{3}\), \(30w\), and \(75w^{5}\) is \(15w\).

Step 4 ：\(\boxed{15w}\) is the final answer.