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.