#1**+5 **

If you are divisible by 9, then you are divisible by 3. Then, the sum of your digits is also divisible by 3.

But you must be even, since you are divisible by 2.

And if you're divisible by 2 and 9, then you are divisible by 18, as well.

So the possibilities are 426, 432, 438, 444 and 448

And 432 is the answer. No other answers are possible because all of the other numbers lie within 18 integers - positive or negative - from 432.

CPhill
Oct 6, 2014

#1**+5 **

Best Answer

If you are divisible by 9, then you are divisible by 3. Then, the sum of your digits is also divisible by 3.

But you must be even, since you are divisible by 2.

And if you're divisible by 2 and 9, then you are divisible by 18, as well.

So the possibilities are 426, 432, 438, 444 and 448

And 432 is the answer. No other answers are possible because all of the other numbers lie within 18 integers - positive or negative - from 432.

CPhill
Oct 6, 2014