Hi, I’m just starting with my GRE prep. I have been using PrepSwift for a week now. I came across the topic of numbers in factorials and couldn’t understand what exactly a “limiting factor” is. Also, why are we considering only one factor? For example, find the powers of 15 in 200!? We use the prime factorization for 15 and get 3x5. As per the solution, the limiting factor is 5. Why do we solely focus on powers of 5 in 200! when there is a 3 as well in the prime factorization of 15.
200! = 3^{97} \cdot 5^{49} \cdot k, where k is the product of all the other prime factors. As you can see, there are more 3’s than 5’s; hence, 5 is the ‘limiting factor.