Final answer:
The GCF of 24 and 30 is 6, while the LCM is 120.
Step-by-step explanation:
To find the greatest common factor (GCF) and least common multiple (LCM) of 24 and 30, we can start by finding the prime factorization of each number:
Prime factorization of 24: 2 x 2 x 2 x 3
Prime factorization of 30: 2 x 3 x 5
The GCF is the product of the common prime factors raised to the lowest exponent: GCF = 2 x 3 = 6
The LCM is the product of all the prime factors, including duplicates, raised to the highest exponent: LCM = 2 x 2 x 2 x 3 x 5 = 120