It's more of a question of what's the definition of factor. To my understanding, for a number 25, 1,5,25 would be the factor because 1*25=25and 5*5=25. It is a question from GRE official guide book and the answer is 58. I don't have difficulty in understanding what the answer is doing, it says 58 is the least number that is not a prime and doesn't contain factors from 1 to 25. What makes me feel uncomfortable is how this answer is related to the question. Obviously the factor of 25! will be 1,2,...,25. And the least that is not a prime would be 4 because I remember we don't count 1 as a prime. Even if the answer is 58, shouldn't the question be framed as something like:
What is the least integer that is not a prime and has no factors same to the factor of 25!?
In fact, I put 26 as the answer because I think 25! has factor 1,2,...,25 but 26 is not one of these factors and it is also a prime. I think I misunderstood what the question is asking about but I can't figure out what exactly is the problem.