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What is the greatest common factor of
60w,36w^(2), and
24w^(4) ?

What is the greatest common factor of $60 \mathrm{w}, 36 w^{2}$ , and $24 w^{4}$ ?

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Greatest common factor of three or four numbers

Full solution

Q. What is the greatest common factor of

60 \mathrm{w}, 36 w^{2}

, and

24 w^{4}

?

Identify prime factors: Identify the prime factors of $60w$ . $\newline$ $60w = 2^2 \times 3 \times 5 \times w$
Find common factors: Identify the prime factors of $36w^2$ . $\newline$ $36w^2 = 2^2 \times 3^2 \times w^2$
Calculate GCF: Identify the prime factors of $24w^4$ . $\newline$ $24w^4 = 2^3 \times 3 \times w^4$
Calculate GCF: Identify the prime factors of $24w^4$ . $\newline$ $24w^4 = 2^3 \times 3 \times w^4$ Find the common prime factors and their lowest powers. $\newline$ The common prime factors are $2$ , $3$ , and $w$ . The lowest powers of these factors in the given numbers are $2^2$ , $3$ , and $w$ .
Calculate GCF: Identify the prime factors of $24w^4$ .
$24w^4 = 2^3 \times 3 \times w^4$ Find the common prime factors and their lowest powers.
The common prime factors are $2$ , $3$ , and $w$ . The lowest powers of these factors in the given numbers are $2^2$ , $3$ , and $w$ . Multiply the common prime factors to find the GCF.
GCF = $2^2 \times 3 \times w = 4 \times 3 \times w = 12w$

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