TITLE: Minimum value of $4$-digit number divided by sum of its digits?
QUESTION [9 upvotes]: If x was a positive 4 digit number and you divide it by the sum of its digits to get the smallest value possible, what is the value of x? For example (1234 = 1234/10)
I got 1099 as my answer however I don't know if this is right or how to prove it.

REPLY [3 votes]: I used Python to prove that shortest posible value is '1099'.

m = []

for eve in range(1000, 10000):

    nums = list(map(int, list(str(eve))))
    m.append((nums, eve / sum(nums)))

m.sort(key=lambda x: x[1])

print(m[0])