#20 - Factorial digit sum

07 Aug 2015 in Project Euler on 5%

$n!$ means $n\times (n-1)\times\cdots\times 3\times 2\times 1$.

For example, $10! = 10\times 9\times\cdots\times 3\times 2\times 1 = 3628800$, and the sum of the digits in the number $10!$ is 3 + 6 + 2 + 8 + 8 + 0 + 0 = 27.

Find the sum of the digits in the number $100!$.

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As said before, Python can very easily handle large numbers. We write a simple loop to calculate $n!$ (though there is one built into the math package). To extract the digits, we convert the number into a string, and map the int function in each element.

# file: "problem020.py"
def factorial(n):
    product = 1
    for i in range(2, n + 1):
        product *= i
    return product
n = 100
fact = factorial(n)
s = sum([int(chara) for chara in str(fact)])
print(s)

At the end, the output is

648
9.362962962962964e-05 seconds.

Thus, the sum is 648.