Final answer:
The greatest common factor (GCF) of 78u^4v^3w^3 and 30u^4vw is 6u^4vw. The options provided do not match the correct GCF, suggesting either an error in the question or the given options.
Step-by-step explanation:
The greatest common factor (GCF) of two algebraic expressions can be found by identifying the highest powers of common factors in their prime factorization that both expressions share. To find the GCF of 78u4v3w3 and 30u4vw, we should first factor the numerical coefficients (78 and 30) and then consider the smallest powers of the variables present in both expressions.
- Prime factorization of 78: 2 x 3 x 13
- Prime factorization of 30: 2 x 3 x 5
- Common numerical factor: 2 x 3 = 6
- Common variable factors: u4 (smallest power of u is 4), v1 (smallest power of v is 1), w1 (smallest power of w is 1)
Therefore, the GCF is 6u4vw.
Looking at the options provided, none of them match the correct GCF. This indicates that the options listed are incorrect or there has been a mistake in the question. The correct GCF should be 6u4vw, which is not listed in the options A, B, C, or D.