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What is the greatest common factor of
30b^(2),80b^(2), and
20b^(3) ?

What is the greatest common factor of $30 b^{2}, 80 b^{2}$ , and $20 b^{3}$ ?

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Greatest common factor of three or four numbers

Full solution

Q. What is the greatest common factor of

30 b^{2}, 80 b^{2}

, and

20 b^{3}

?

List Prime Factors: List the prime factors of each term. $\newline$ $30b^2 = 2 \times 3 \times 5 \times b \times b$ $\newline$ $80b^2 = 2 \times 2 \times 2 \times 2 \times 5 \times b \times b$ $\newline$ $20b^3 = 2 \times 2 \times 5 \times b \times b \times b$
Identify Common Factors: Identify the common prime factors in all three terms. $\newline$ The common prime factors are $2$ , $5$ , $b$ , and $b$ (since $b^2$ is the lowest power of $b$ common to all terms).
Find Greatest Common Factor: Multiply the common prime factors to find the greatest common factor (GCF). $\newline$ GCF = $2 \times 5 \times b \times b = 10b^2$

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