This quiz is about for loops, while loops and vectorization in MATLAB.

**1. ** Write a function that takes an input integer, and computes its factorial,

in the following ways:

(a) Write this function using while-loop. Name it `getFacWhile(n)`

.

(b) Write this function using for-loop. Name it `getFacFor(n)`

.

(c) Write this function using the vectorization concept. Name it `getFacVec(n)`

. (Hint: for the vectorized version of this function, you will have to first create a vector of integers from 1 to n, using MATLAB vector construction notation (This is very simple and easy if you recall from lecture notes). Then use MATLAB’s built-in prod() function to accomplish the task of computing $n!$ as given by the above equation.)

**2. ** Write a MATLAB script, `timeFacFuncs.m`

that times the performance of the three functions you wrote in the previous problem, so that when you run this script, you get an output like the following,

```
>> timeFacFuncs
average runtime for getFacWhile(1700000): 0.0054129 seconds
average runtime for getFacFor(1700000): 0.0080964 seconds
average runtime for getFacVec(1700000): 0.005283 seconds
```

**3. ** **Extra Credit** Modify your answer to problem 1.(c) above in such a way that instead of using `prod()`

, you get the factorial using `sum()`

and some other elementary mathematical MATLAB functions. (Hint: for this problem, you will need to transform the numbers involved in calculations using some appropriate MATLAB mathematical function and revert the result at the end.)