Question

How many factors does 7^11*19^6*79^23 have?

Answer 1

How many factors, or how many prime factors? There are obviously 11+6+23 prime factors. Just add up all the exponents.

Now, if you want factors in general, that's a little more complicated.

There are 11+1 ways to choose subsets of 7^11 (choosing none is also an option)
There are 6+1 ways to choose subsets of 19^6
There are 23+1 ways to choose subsets of 79^23

So, the number of factors, including 1 is 12*7*24 = 2016