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Find the greatest common factor of these three expressions.
3w^(4),10w^(2), and 6

Find the greatest common factor of these three expressions. $\newline$ $3 w^{4}, 10 w^{2} \text {, and } 6$

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Estimate positive and negative square roots

Full solution

Q. Find the greatest common factor of these three expressions.

\newline

3 w^{4}, 10 w^{2} \text {, and } 6

Identify Factors: First, we need to identify the factors of each individual term. $\newline$ For $3w^4$ , the factors are $3$ and $w^4$ . $\newline$ For $10w^2$ , the factors are $2$ , $5$ , and $w^2$ . $\newline$ For $6$ , the factors are $2$ and $3$ .
Find Common Factors: Next, we look for common factors among all three expressions. $\newline$ The common numerical factor is $3$ , as it is present in $3w^4$ and $6$ but not in $10w^2$ . $\newline$ However, since $10w^2$ has a factor of $2$ , and $6$ has a factor of $2$ , we cannot include $3$ as the greatest common factor. $\newline$ The common variable factor is $w^2$ , as it is the highest power of $3w^4$ $0$ that is present in both $3w^4$ and $10w^2$ .
Combine to Find GCF: Now, we combine the common factors to find the greatest common factor (GCF). The GCF is the product of all common factors. Since the only common variable factor is $w^2$ , and there is no common numerical factor among all three expressions, the GCF is $w^2$ .

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