An easier math problem for the day

Yesterday was intense, wasn't it? My brain is still a little overloaded, really. We'll take it down a notch with something simpler:

What is the largest integer that can be obtained as the product as the product of positive integers that add up to 100?

This starts out simple: pick any numbers you can think of that add up to 100. 50 + 50 works, right? So what is their product? 50 * 50 = 2500.

What about two different numbers, like 49 and 51? That's 2499. 25 and 75? That's no better, it's 1875. Seems that numbers that are equal will maximize efficiency.

Well, what about 4 equal numbers, like 25 * 25 * 25 *25? Well, we get 390625. That's way better.  So, 5 numbers? 20⁵ =3,200,000. Uh. How far can you keep going along with this pattern until you get the biggest number possible? And is there some sort of algorithm or process to make looking for the answer easier?