How do you determine the total amount of positive factors of a number

Part of a homework assignment I'm stuck on from my discrete math class. I suspect this may belong in another forum, but I wasn't sure which one.

Part a.) Find the prime factorization of 7056. *okay.. no problem*

$\displaystyle 7056 = 2 * 3528 = 2^2 * 1764 = 2^3 * 882 = 2^4 * 441 = 2^4 * 3 * 147 = 2^4 * 3^2 * 49 = 2^4 * 3^2 * 7^2$

Part b.) How many positive factors are there of 7056?

I'm stuck on this, I used an example of a previous question from the homework where I discovered that:

$\displaystyle 48 = 2^4 * 3$ and that it has 10 positive factors. (namely 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48) and 10 negative identical factors.

I can't seem to derive the method to determine total factors based on the powers of each individual factor. I certainly don't want to write them all out. My best guess is 36, which i figured by adding each exponent, then adding each exponent multiplied to the other exponents, in turn, then adding all three exponents multiplied. (1+4+2+2+1)+(4*2+4*2+2*2)+(4*2*2)=10+20+16=36

something seems fishey about my methodology though..

Thanks for the help!