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Find the greatest common factor.\newline10w,2w210w, 2w^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.\newline10w,2w210w, 2w^2\newlineWrite your answer as a constant times a product of single variables raised to exponents.\newline__\_\_
  1. Factorization of 1010w: First find the complete factorization of 1010w.\newline10=2×510 = 2 \times 5\newlinew=ww = w\newline10w=2×5×w10w = 2 \times 5 \times w
  2. Factorization of 2w22w^2: Now, find the complete factorization of 2w22w^2.\newline2=22 = 2\newlinew2=w×ww^2 = w \times w\newline2w2=2×w×w2w^2 = 2 \times w \times w
  3. Find Greatest Common Factor: We found:\newline10w=2×5×w10w = 2 \times 5 \times w\newline2w2=2×w×w2w^2 = 2 \times w \times w\newlineFind the greatest common factor of 10w10w and 2w22w^2.\newlineCommon factors are 22 and ww.\newline2×w=2w2 \times w = 2w\newlineGreatest common factor: 2w2w

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