Minimum Digit Sum Fraction

Algebra Level 3

Let S(N)S(N) denote the digit sum of the integer NN. As NN ranges over all 3-digit positive numbers, what value of NN would give the minimum of M=NS(N)M = \frac{N}{S(N)}?

Details and assumptions

The number 12=01212=012 is a 2-digit number, not a 3-digit number.

The digit sum of a number is the sum of all its digits. For example the digit sum of 1123 is 1+1+2+3=71 + 1 + 2 + 3 = 7.

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