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What is the greatest common factor of
35b^(2),15b^(3), and
5b ?

What is the greatest common factor of $35 b^{2}, 15 b^{3}$ , and $5 b$ ?

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Greatest common factor of three or four numbers

Full solution

Q. What is the greatest common factor of

35 b^{2}, 15 b^{3}

, and

5 b

?

List prime factors: List the prime factors of each term. $\newline$ $35b^2 = 5 \times 7 \times b \times b$ $\newline$ $15b^3 = 3 \times 5 \times b \times b \times b$ $\newline$ $5b = 5 \times b$
Identify common factors: Identify the common prime factors in all three terms. $\newline$ The common prime factors are $5$ and $b$ .
Determine lowest powers: Determine the lowest power of the common prime factors in each term. $\newline$ The lowest power of $5$ is $5^1$ (since all terms have at least one $5$ ). $\newline$ The lowest power of b is $b^1$ (since the term $5b$ has only one b).
Find GCF: Multiply the common prime factors with their lowest powers to find the GCF. $\newline$ GCF = $5^1 \times b^1$ $\newline$ GCF = $5b$

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