2026/019) Determine all positive integers that are equal to 300 times the sum of their digits.

 

The number must end with 2 zeroes . Excluding the 2 zeroes the sum of digits multiplied by 3 is the number. It is not one digit number as multiplied by 3 of the digit changed number

Maximum sum of digits of a 3 digits number is 27. Multiplied by 3 gives 81 which is a 2 digits number . So number of digits cannot be 3 or more. So it is a 2 digit number if it exists. 

Let it be $10a +b$. 

We have 

$10a +b =3(a+b)$ 

Or $7a =2b$ 

As a and b are single digit number so a is 2 and b is 7 and number is 27. We have removed 2 zeroes and so number is 2700 .