#### Jomo

##### Elite Member

- Joined
- Dec 30, 2014

- Messages
- 3,529

Here is my work.

Let the three digit number be 100a + 10b +1c. a is not 0 since we want a three digit number. Also b and c are non zero as the sum. a+b+c

__>__1, while abc will be 0 if b or c is 0.

Therefore the smallest number we can use is 111. Now 11x will not work as the sum is x+2 and the product is x

What about 12X? The sum is 3+x and the product is 2x. Now if 3+x=2x, then x=3. So the smallest number with the desired property is 123.

What is the better way to do this??