How many distinct factors can be made from the number $2^5*3^4*5^3*7^2*11^1$? How many distinct factors can be made from the number $2^5*3^4*5^3*7^2*11^1$?
Hmmm... So I didn't know what to do here so I tested some cases for a rule. 
If a number had the factors $3^2$ and $2^1$, you can make $5$ distinct factors: $2^1$, $3^1$, $3^2$, $2^1 \cdot 3^1$, $2^1 \cdot 3^2$... I don't see a pattern yet.
How does one go about this?
I don't think the answer is $5!$....

The number you are talking about is $2^5\cdot3^4\cdot4^3\cdot3^2\cdot2^1$  if i understand what you write.
You can write this number as $ 2^5\cdot3^4\cdot2^6\cdot3^2\cdot2^1=2^{12}\cdot3^6$ which is a product of prime numbers.
So,the number of distinct factors is exactly $$(12+1)\cdot(6+1)=91$$.
You should look here
 for more details and to see how to solve any similar problem.
