Final answer:
To find the GCF of 30g⁴h³ and 42g⁴h², factorize both expressions and find their common factors.
Step-by-step explanation:
To find the greatest common factor (GCF) of 30g⁴h³ and 42g⁴h², we need to factorize both expressions. The GCF is the product of the common factors raised to their lowest exponent.
The prime factorization of 30 is 2 * 3 * 5. The prime factorization of 42 is 2 * 3 * 7. The variables g⁴h³ and g⁴h² have a common factor of g⁴h².
So, the GCF of 30g⁴h³ and 42g⁴h² is 2 * 3 * g⁴h², which simplifies to 6g⁴h².