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gcf of $14c^3$ , $70c^4$ , $28c^2$

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Factor quadratics

Full solution

Q. gcf of

14c^3

,

70c^4

,

28c^2

Identify Coefficients and GCF: Identify the numerical coefficients of each term and find their GCF. $\newline$ The numerical coefficients are $14$ , $70$ , and $28$ . $\newline$ To find the GCF of these numbers, list the factors of each: $\newline$ Factors of $14$ : $1$ , $2$ , $7$ , $14$ $\newline$ Factors of $70$ : $1$ , $2$ , $70$ $1$ , $7$ , $70$ $3$ , $14$ , $70$ $5$ , $70$ $\newline$ Factors of $28$ : $1$ , $2$ , $28$ $0$ , $7$ , $14$ , $28$ $\newline$ The greatest common factor of $14$ , $70$ , and $28$ is $14$ .
Identify Smallest Power: Identify the smallest power of $c$ in each term to find the GCF for the variable part. $\newline$ The powers of $c$ are $c^3$ , $c^4$ , and $c^2$ . $\newline$ The smallest power of $c$ is $c^2$ .
Combine GCF for Overall: Combine the GCF of the numerical coefficients with the GCF of the variable part to find the overall GCF. $\newline$ The GCF of the numerical coefficients is $14$ . $\newline$ The GCF of the variable part is $c^2$ . $\newline$ Therefore, the GCF of $14c^3$ , $70c^4$ , and $28c^2$ is $14c^2$ .

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