A special 3-digit number

Number Theory Level 5

Let \(S(N) \) denote the digit sum of the integer \(N\). Let \(R\) denote the smallest integer value of \( \frac {N} {S(N)} \), where \(N\) is a 3-digit number. What is the largest 3-digit number \(N\) that satisfies \( \frac {N}{S(N)} = R\)?

Details and assumptions

The digit sum of an integer is the sum of all its digits. For example, the digit sum of \(N = 1123\) is \(1+1+2+3=7\).

The number \(12=012\) is a 2-digit number, not a 3-digit number.


Problem Loading...

Note Loading...

Set Loading...