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Find the greatest common factor.\newline6n3,9n36n^3, 9n^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.\newline6n3,9n36n^3, 9n^3\newlineWrite your answer as a constant times a product of single variables raised to exponents.\newline__\_\_
  1. Factorization of 6n36n^3: First, find the complete factorization of 6n36n^3.\newline6=2×36 = 2 \times 3\newlinen3=n×n×nn^3 = n \times n \times n\newlineTherefore, 6n3=2×3×n×n×n6n^3 = 2 \times 3 \times n \times n \times n
  2. Factorization of 9n39n^3: Next, find the complete factorization of 9n39n^3. \newline9=3×39 = 3 \times 3\newlinen3=n×n×nn^3 = n \times n \times n\newlineTherefore, 9n3=3×3×n×n×n9n^3 = 3 \times 3 \times n \times n \times n
  3. Greatest Common Factor: Now, find the greatest common factor of 6n36n^3 and 9n39n^3. The common factors are 33, nn, nn, and nn. Therefore, the greatest common factor is 3×n×n×n=3n33 \times n \times n \times n = 3n^3

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