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Find the greatest common factor.\newline6y3,9y36y^3, 9y^3\newlineWrite your answer as a constant times a product of single variables raised to exponents.\newline__\_\_

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Full solution

Q. Find the greatest common factor.\newline6y3,9y36y^3, 9y^3\newlineWrite your answer as a constant times a product of single variables raised to exponents.\newline__\_\_
  1. Find Factorization of 6y36y^3: First, find the complete factorization of 6y36y^3.\newline6=2×36 = 2 \times 3\newliney3=y×y×yy^3 = y \times y \times y\newlineTherefore, 6y3=2×3×y×y×y6y^3 = 2 \times 3 \times y \times y \times y.
  2. Find Factorization of 9y39y^3: Next, find the complete factorization of 9y39y^3. \newline9=3×39 = 3 \times 3\newliney3=y×y×yy^3 = y \times y \times y\newlineTherefore, 9y3=3×3×y×y×y9y^3 = 3 \times 3 \times y \times y \times y.
  3. Find Greatest Common Factor: Now, find the greatest common factor of 6y36y^3 and 9y39y^3. The common factors are 33, yy, yy, and yy. Therefore, the greatest common factor is 3×y×y×y=3y33 \times y \times y \times y = 3y^3.

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