What is the number of a three digit number, which is 18 times the sum of hundreds, tens and ones, equal to itself?

What is the number of a three digit number, which is 18 times the sum of hundreds, tens and ones, equal to itself?

18 times the sum of the hundreds, tens and ones of a three digit number is equal to itself
So, this number is even and divisible by 9
So the sum of hundreds, tens and ones can be divided by nine
So, the sum of the hundred, the ten and the individual may be 27, 18 and 9
When the sum of hundreds, tens and individuals is 27, the original number is 999, which is odd
When the sum of hundreds, tens and individuals is 18, 18 * 18 = 324, 3 + 2 + 4 = 9 ≠ 18, which is not suitable for the topic
9 * 18 = 162,1 + 6 + 2 = 9 when the sum of hundred, ten and individual digits is 9
So, the original number is 162