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Find the greatest common factor.\newline6t3,9t6t^3, 9t\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.\newline6t3,9t6t^3, 9t\newlineWrite your answer as a constant times a product of single variables raised to exponents.\newline__\_\_
  1. Factorization of 6t36t^3: First find the complete factorization of 6t36t^3.\newline6=2×36 = 2 \times 3\newlinet3=t×t×tt^3 = t \times t \times t\newline6t3=2×3×t×t×t6t^3 = 2 \times 3 \times t \times t \times t
  2. Factorization of 9t9t: Now, find the complete factorization of 9t9t.9=3×39 = 3 \times 3t=tt = t9t=3×3×t9t = 3 \times 3 \times t
  3. Find Greatest Common Factor: We found:\newline6t3=2×3×t×t×t6t^3 = 2 \times 3 \times t \times t \times t\newline9t=3×3×t9t = 3 \times 3 \times t\newlineFind the greatest common factor of 6t36t^3 and 9t9t.\newlineCommon factors are 33 and tt.\newline3×t=3t3 \times t = 3t\newlineGreatest common factor: 3t3t

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