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Find the greatest common factor.\newline6h3,10h26h^3, 10h^2\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.\newline6h3,10h26h^3, 10h^2\newlineWrite your answer as a constant times a product of single variables raised to exponents.\newline__\_\_
  1. Factorization of 6h36h^3: First find the complete factorization of 6h36h^3.\newline6=2×36 = 2 \times 3\newlineh3=h×h×hh^3 = h \times h \times h\newline6h3=2×3×h×h×h6h^3 = 2 \times 3 \times h \times h \times h
  2. Factorization of 10h210h^2: Now, find the complete factorization of 10h210h^2. \newline10=2×510 = 2 \times 5\newlineh2=h×hh^2 = h \times h\newline10h2=2×5×h×h10h^2 = 2 \times 5 \times h \times h
  3. Find Greatest Common Factor: We found:\newline6h3=2×3×h×h×h6h^3 = 2 \times 3 \times h \times h \times h\newline10h2=2×5×h×h10h^2 = 2 \times 5 \times h \times h\newlineFind the greatest common factor of 6h36h^3 and 10h210h^2.\newlineCommon factors are 22, hh, and hh.\newline2×h×h=2h22 \times h \times h = 2h^2\newlineGreatest common factor: 2h22h^2

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