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What is the greatest common factor of
35y^(4),14y^(4), and
63y^(4) ?

What is the greatest common factor of $35 y^{4}, 14 y^{4}$ , and $63 y^{4}$ ?

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Greatest common factor of three or four numbers

Full solution

Q. What is the greatest common factor of

35 y^{4}, 14 y^{4}

, and

63 y^{4}

?

List prime factors: List the prime factors of each number without the variable part. $\newline$ Prime factors of $35$ : $5 \times 7$ $\newline$ Prime factors of $14$ : $2 \times 7$ $\newline$ Prime factors of $63$ : $3 \times 3 \times 7$
Identify common factors: Identify the common prime factors from the prime factorization of the numbers. $\newline$ The common prime factor is $7$ .
Include variable part: Since the variable part is the same for all terms $y^{4}$ , we include it in the GCF. $\newline$ The variable part is $y^{4}$ .
Multiply to find GCF: Multiply the common prime factor by the variable part to find the GCF. $\newline$ GCF = $7 \times y^{4}$
Verify GCF: Verify that the GCF is indeed a factor of all three terms. $\newline$ $\frac{35y^{4}}{7y^{4}} = 5y^{0} = 5$ $\newline$ $\frac{14y^{4}}{7y^{4}} = 2y^{0} = 2$ $\newline$ $\frac{63y^{4}}{7y^{4}} = 9y^{0} = 9$ $\newline$ Since all results are whole numbers, the GCF is correct.

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