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Exercise 9

Don't let the math scare you. This is a logic and syntax problem, not a math problem.

Write a function that computes and returns the factorial of a number by using a for or while loop. The factorial of a positive integer n, signified by n!, is defined as the product of all integers between 1 and n, inclusive:

n!	Expansion	Result
`1!`	`1`	1
`2!`	`1 * 2`	2
`3!`	`1 * 2 * 3`	6
`4!`	`1 * 2 * 3 * 4`	24
`5!`	`1 * 2 * 3 * 4 * 5`	120

You may assume that the argument is always a positive integer.

print(factorial(1))   # 1
print(factorial(2))   # 2
print(factorial(3))   # 6
print(factorial(4))   # 24
print(factorial(5))   # 120
print(factorial(6))   # 720
print(factorial(7))   # 5040
print(factorial(8))   # 40320
print(factorial(25))  # 15511210043330985984000000

Solution

def factorial(n):
    result = 1
    while n > 0:
        result *= n
        n -= 1

    return result

def factorial(n):
    result = 1
    for number in range(n, 0, -1):
        result *= number

    return result

Our first solution uses a while loop to compute the return value. We begin by assigning the result variable to 1, then we multiply result by all of the integers between n and 1, inclusive. Note that we need to decrement n by 1 at the end of each iteration.

The second solution is similar, but it uses a for loop instead of a while loop. The benefit of using for is that we don't need to worry about decrementing n. Instead, we just iterate over the integers between n and 1, inclusive, using a range.

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