Final answer:
The greatest common factor (GCF) of 42a³b, 48a²b², and 24ab³ is obtained by finding the lowest powers of common factors in each expression. By breaking down each term into its prime factors, we find that the GCF is 6ab.
Step-by-step explanation:
The greatest common factor (GCF) of the expressions 42a³b, 48a²b², and 24ab³ is obtained by finding the highest power of common factors in the given expressions. To determine the GCF, we break down each term into its prime factors and include the lowest power of each common factor.
- 42a³b = 2 × 3 × 7 × a³ × b
- 48a²b² = 2´ × 3 × a² × b²
- 24ab³ = 2³ × 3 × a × b³
The common factors are 2, 3, a, and b. The lowest powers among the expressions are 2¹ (from 24ab³), 3¹ (common to all), a¹ (from 24ab³), and b¹ (from 42a³b). Thus, the GCF is 2¹ × 3¹ × a¹ × b¹, which simplifies to 6ab.