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Find the greatest common factor (GCF ) of 25a^(3)b,20a^(2)b^(2), and 45ab^(3).

User Papillon
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Final answer:

The GCF of 25a^3b, 20a^2b^2, and 45ab^3 is 5ab.

Step-by-step explanation:

The greatest common factor (GCF) is the largest number that divides evenly into all of the given numbers. To find the GCF of 25a^3b, 20a^2b^2, and 45ab^3, we need to find the common factors of each term and choose the smallest exponent for each variable.

Let's break down each term into its prime factors:

  • 25a^3b = 5 * 5 * a * a * a * b
  • 20a^2b^2 = 2 * 2 * 5 * a * a * b * b
  • 45ab^3 = 3 * 3 * 5 * a * b * b * b

The common factors are 5, a, and b. To determine the smallest exponent for each variable, we take the lowest exponent:

  • For 5, the smallest exponent is 1.
  • For a, the smallest exponent is 1.
  • For b, the smallest exponent is 1.

Therefore, the greatest common factor (GCF) is 5ab.

User Colin Bacon
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