Starbucks' 87,000 options

I picked up a nutrition facts pamphlet at Starbucks that promises that with all the choices of creamer, syrup, spices, etc. "87,000" different beverages are possible.

Here's a computer science/reverse engineering problem. Find the number that is most likely to be the exact value of the number of options as Starbucks calculates it. Some things you might assume:

1. It's likely to be within 500 of 87,000.
2. It's factorization makes it look the most like the product of 2's, 3's or other small numbers reflecting many choices. For instance, it's unlikely to be 87011, which is prime. However, 87480 is a candidate since 87480 = 2 * 2 * 2 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 5. It's possible that there are 3 ingredients which you can have or not, explaining the 3 twos. Maybe there are 3 sizes, 2 types of toppings (and the option to have nothing), 2 kinds of creamer (or none), something else with 5 options, and finally 27 (3*3*3) different beverages. I don't know if this is how the Starbucks menu works and it doesn't matter: 87480 is definitely more likely than 87011.

I'd like to hear of good algorithms to solve this problem, and if anyone who reads this knows more about Starbucks, that's a fine way to answer too.

If we can't figure it out, let's not sweat it. I'm pretty sure that 87,000 is way too low anyway...