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What is the greatest common factor of
20a^(2),12a^(2), and
8a ?

What is the greatest common factor of $20 a^{2}, 12 a^{2}$ , and $8 a$ ?

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Greatest common factor of three or four numbers

Full solution

Q. What is the greatest common factor of

20 a^{2}, 12 a^{2}

, and

8 a

?

List prime factors: List the prime factors of each term. $\newline$ For $20a^{2}$ , the prime factors are $2 \times 2 \times 5 \times a \times a$ . $\newline$ For $12a^{2}$ , the prime factors are $2 \times 2 \times 3 \times a \times a$ . $\newline$ For $8a$ , the prime factors are $2 \times 2 \times 2 \times a$ .
Identify common factors: Identify the common prime factors. $\newline$ The common prime factors of $20a^{2}$ , $12a^{2}$ , and $8a$ are $2 \times 2 \times a$ , since these are the only prime factors that appear in all three terms.
Calculate GCF: Calculate the greatest common factor (GCF). $\newline$ The GCF is the product of the common prime factors. Therefore, the GCF of $20a^{2}$ , $12a^{2}$ , and $8a$ is $2 \times 2 \times a$ , which is $4a$ .

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