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What is the greatest common factor of 
30b^(2),80b^(2), and 
20b^(3) ?

What is the greatest common factor of 30b2,80b2 30 b^{2}, 80 b^{2} , and 20b3 20 b^{3} ?\newline

Full solution

Q. What is the greatest common factor of 30b2,80b2 30 b^{2}, 80 b^{2} , and 20b3 20 b^{3} ?\newline
  1. List Coefficients and Powers: Step Title: List the Coefficients and Powers of bb Concise Step Description: Identify the numerical coefficients and the powers of bb in each term. Step Calculation: Coefficients are 3030, 8080, and 2020. Powers of bb are b2b^2, b2b^2, and b3b^3.
  2. Find GCF of Coefficients: Step Title: Find the GCF of the Coefficients\newlineConcise Step Description: Calculate the greatest common factor of the numerical coefficients.\newlineStep Calculation: GCF of 3030, 8080, and 2020 is 1010.
  3. Determine Lowest Power: Step Title: Determine the Lowest Power of bb Concise Step Description: Identify the lowest power of bb common to all terms. Step Calculation: The lowest power of bb common in all terms is b2b^2.
  4. Combine GCF and Power: Step Title: Combine the GCF of Coefficients and Lowest Power of bb\newlineConcise Step Description: Multiply the GCF of the coefficients by the lowest power of bb to find the overall GCF.\newlineStep Calculation: The greatest common factor is 10b210b^2.