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What is the greatest common factor of
8m^(2),4m, and
10m^(4) ?

What is the greatest common factor of $8 m^{2}, 4 m$ , and $10 m^{4}$ ?

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Greatest common factor of three or four numbers

Full solution

Q. What is the greatest common factor of

8 m^{2}, 4 m

, and

10 m^{4}

?

List Prime Factors: List the prime factors of each term. $\newline$ For $8m^2$ , the prime factors are $2^3 \times m^2$ . $\newline$ For $4m$ , the prime factors are $2^2 \times m$ . $\newline$ For $10m^4$ , the prime factors are $2 \times 5 \times m^4$ .
Identify Common Factors: Identify the common prime factors. $\newline$ The common prime factors of $8m^2$ , $4m$ , and $10m^4$ are $2$ and $m$ , since these are the only prime factors that appear in all three terms.
Determine Lowest Power: Determine the lowest power of the common prime factors. $\newline$ The lowest power of $2$ that appears in all terms is $2^1$ (from $10m^4$ ). $\newline$ The lowest power of $m$ that appears in all terms is $m^1$ (from $4m$ ).
Find GCF: Multiply the common prime factors with their lowest powers to find the GCF. $\newline$ The GCF is $2^1 \times m^1$ , which simplifies to $2m$ .

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