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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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Prime factorization

Full solution

Q. Find the greatest common factor of these three expressions

\newline

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

Identify Coefficients and Powers: Identify the numerical coefficients and the powers of $w$ in each expression. $\newline$ - Coefficients: $3$ , $10$ , $6$ $\newline$ - Powers of $w$ : $w^{4}$ , $w^{2}$ , no $w$ in $6$
Find GCF of Coefficients: Find the GCF of the numerical coefficients $3$ , $10$ , and $6$ . $\newline$ - Factors of $3$ : $1$ , $3$ $\newline$ - Factors of $10$ : $1$ , $2$ , $5$ , $10$ $\newline$ - Factors of $6$ : $1$ , $2$ , $3$ , $6$ $\newline$ - Common factors: $1$ $\newline$ - GCF of coefficients: $1$
Determine Smallest Common Power: Determine the smallest power of $w$ common to all terms. $\newline$ - The term $6$ does not contain $w$ , so the smallest power of $w$ common to all terms is $w^0$ , which is $1$ .

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