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Find the greatest common factor.\newline9w3,6w39w^3, 6w^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.\newline9w3,6w39w^3, 6w^3\newlineWrite your answer as a constant times a product of single variables raised to exponents.\newline__\_\_
  1. Factorization of 9w39w^3: First find the complete factorization of 9w39w^3.\newline9=3×39 = 3 \times 3\newlinew3=w×w×ww^3 = w \times w \times w\newlineTherefore, 9w3=3×3×w×w×w9w^3 = 3 \times 3 \times w \times w \times w.
  2. Factorization of 6w36w^3: Now, find the complete factorization of 6w36w^3.\newline6=2×36 = 2 \times 3\newlinew3=w×w×ww^3 = w \times w \times w\newlineTherefore, 6w3=2×3×w×w×w6w^3 = 2 \times 3 \times w \times w \times w.
  3. Find Greatest Common Factor: We found:\newline9w3=3×3×w×w×w9w^3 = 3 \times 3 \times w \times w \times w\newline6w3=2×3×w×w×w6w^3 = 2 \times 3 \times w \times w \times w\newlineFind the greatest common factor of 9w39w^3 and 6w36w^3.\newlineCommon factors are 33, ww, ww, and ww.\newline3×w×w×w=3w33 \times w \times w \times w = 3w^3\newlineGreatest common factor: 3w33w^3

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