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Find the greatest common factor.\newline10m3,8m310m^3, 8m^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.\newline10m3,8m310m^3, 8m^3\newlineWrite your answer as a constant times a product of single variables raised to exponents.\newline__\_\_
  1. Factorization of 10m310m^3: First find the complete factorization of 10m310m^3.\newline10=2×510 = 2 \times 5\newlinem3=m×m×mm^3 = m \times m \times m\newline10m3=2×5×m×m×m10m^3 = 2 \times 5 \times m \times m \times m
  2. Factorization of 8m38m^3: Now, find the complete factorization of 8m38m^3. \newline8=2×2×28 = 2 \times 2 \times 2\newlinem3=m×m×mm^3 = m \times m \times m\newline8m3=2×2×2×m×m×m8m^3 = 2 \times 2 \times 2 \times m \times m \times m
  3. Common Factor Calculation: We found:\newline10m3=2×5×m×m×m10m^3 = 2 \times 5 \times m \times m \times m\newline8m3=2×2×2×m×m×m8m^3 = 2 \times 2 \times 2 \times m \times m \times m\newlineFind the greatest common factor of 10m310m^3 and 8m38m^3.\newlineThe common factors are 22, mm, mm, and mm.\newline2×m×m×m=2m32 \times m \times m \times m = 2m^3\newlineGreatest common factor: 2m32m^3

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