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Find the greatest common factor.\newline6j3,9j36j^3, 9j^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.\newline6j3,9j36j^3, 9j^3\newlineWrite your answer as a constant times a product of single variables raised to exponents.\newline__\_\_
  1. Factorization of 6j36j^3: First find the complete factorization of 6j36j^3.\newline6=2×36 = 2 \times 3\newlinej3=j×j×jj^3 = j \times j \times j\newline6j3=2×3×j×j×j6j^3 = 2 \times 3 \times j \times j \times j
  2. Factorization of 9j39j^3: Now, find the complete factorization of 9j39j^3.9=3×39 = 3 \times 3j3=j×j×jj^3 = j \times j \times j9j3=3×3×j×j×j9j^3 = 3 \times 3 \times j \times j \times j
  3. Find Greatest Common Factor: We found:\newline6j3=2×3×j×j×j6j^3 = 2 \times 3 \times j \times j \times j\newline9j3=3×3×j×j×j9j^3 = 3 \times 3 \times j \times j \times j\newlineFind the greatest common factor of 6j36j^3 and 9j39j^3.\newlineCommon factors are 33, jj, jj, and jj.\newline3×j×j×j=3j33 \times j \times j \times j = 3j^3\newlineGreatest common factor: 3j33j^3

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