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Find the greatest common factor.\newline10d3,8d310d^3, 8d^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.\newline10d3,8d310d^3, 8d^3\newlineWrite your answer as a constant times a product of single variables raised to exponents.\newline__\_\_
  1. Factorization of 10d310d^3: First find the complete factorization of 10d310d^3.10=2×510 = 2 \times 5d3=d×d×dd^3 = d \times d \times d10d3=2×5×d×d×d10d^3 = 2 \times 5 \times d \times d \times d
  2. Factorization of 8d38d^3: Now, find the complete factorization of 8d38d^3.8=2×2×28 = 2 \times 2 \times 2d3=d×d×dd^3 = d \times d \times d8d3=2×2×2×d×d×d8d^3 = 2 \times 2 \times 2 \times d \times d \times d
  3. Find Greatest Common Factor: We found:\newline10d3=2×5×d×d×d10d^3 = 2 \times 5 \times d \times d \times d\newline8d3=2×2×2×d×d×d8d^3 = 2 \times 2 \times 2 \times d \times d \times d\newlineFind the greatest common factor of 10d310d^3 and 8d38d^3.\newlineThe common factors are 22, dd, dd, and dd.\newline2×d×d×d=2d32 \times d \times d \times d = 2d^3\newlineGreatest common factor: 2d32d^3

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