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What is the greatest common factor of
6a,8a^(2), and 14 ?

What is the greatest common factor of $6 a, 8 a^{2}$ , and $14$ ?

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Greatest common factor of three or four numbers

Full solution

Q. What is the greatest common factor of

6 a, 8 a^{2}

, and

14

?

Find GCF of $6a$ and $8a^2$ : List the prime factors of each term to find the GCF. $\newline$ Prime factors of $6a$ : $2$ , $3$ , $a$ $\newline$ Prime factors of $8a^2$ : $2$ , $2$ , $2$ , $a$ , $a$ $\newline$ Prime factors of $8a^2$ $2$ : $2$ , $8a^2$ $4$
Identify common prime factors: Identify the common prime factors among all three terms. $\newline$ The common prime factors are: $2$
Determine highest power of common prime factors: Determine the highest power of the common prime factors that is present in all three terms. $\newline$ Since the term $14$ does not have the factor ' $a$ ', ' $a$ ' cannot be part of the GCF. $\newline$ The highest power of $2$ that is present in all three terms is $2^1$ (or just $2$ ).
Combine common prime factors to find GCF: Combine the common prime factors to find the GCF. $\newline$ The GCF is $2$ .

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