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What is the greatest common factor of
14c^(3),70c^(4), and
28c^(2) ?

What is the greatest common factor of $14 c^{3}, 70 c^{4}$ , and $28 c^{2}$ ?

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Greatest common factor of three or four numbers

Full solution

Q. What is the greatest common factor of

14 c^{3}, 70 c^{4}

, and

28 c^{2}

?

List Prime Factors: List the prime factors of each term. $\newline$ For $14c^{3}$ , the prime factors are $2$ , $7$ , and $c$ multiplied by itself three times ( $c*c*c$ ). $\newline$ For $70c^{4}$ , the prime factors are $2$ , $5$ , $7$ , and $c$ multiplied by itself four times ( $2$ $0$ ). $\newline$ For $2$ $1$ , the prime factors are $2$ , $2$ , $7$ , and $c$ multiplied by itself twice ( $2$ $6$ ).
Identify Common Factors: Identify the common prime factors. The common prime factors of $14c^{3}$ , $70c^{4}$ , and $28c^{2}$ are $2$ , $7$ , and at least two $c$ 's because those are the factors they all share.
Determine GCF: Determine the greatest common factor (GCF). The GCF is the product of the common prime factors using the lowest exponent for the variable $c$ found in all terms. Since the term with the lowest exponent of $c$ is $c^{2}$ , we use $c^{2}$ . The GCF is $2 \times 7 \times c^{2} = 14c^{2}$ .

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