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What is the greatest common factor of
15n^(5),30n^(3), and
45n^(2) ?

What is the greatest common factor of $15 n^{5}, 30 n^{3}$ , and $45 n^{2}$ ?

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Greatest common factor of three or four numbers

Full solution

Q. What is the greatest common factor of

15 n^{5}, 30 n^{3}

, and

45 n^{2}

?

List Prime Factors: List the prime factors of each term. $\newline$ For $15n^{5}$ , the prime factors are $3$ , $5$ , and $n^{5}$ . $\newline$ For $30n^{3}$ , the prime factors are $2$ , $3$ , $5$ , and $n^{3}$ . $\newline$ For $45n^{2}$ , the prime factors are $3$ , $3$ (or $3$ $2$ ), $5$ , and $3$ $4$ .
Identify Common Factors: Identify the common prime factors. $\newline$ The common prime factors of $15n^{5}$ , $30n^{3}$ , and $45n^{2}$ are $3$ , $5$ , and the lowest power of $n$ that appears in all terms, which is $n^{2}$ .
Calculate GCF: Calculate the greatest common factor (GCF). $\newline$ The GCF is the product of the common prime factors using the lowest powers of the variables that appear in all terms. $\newline$ GCF = $3 \times 5 \times n^{2} = 15n^{2}$

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